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Polynomials, Expressions, and Formulas Or, How I Learned to Stop Worrying and Love the Variable.

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Presentation on theme: "Polynomials, Expressions, and Formulas Or, How I Learned to Stop Worrying and Love the Variable."— Presentation transcript:

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2 Polynomials, Expressions, and Formulas Or, How I Learned to Stop Worrying and Love the Variable

3 Overview We begin this module with a study of numbers and the basic operations of addition, subtraction, multiplication, and division. The algebraic properties of these operations are introduced along with the conventions for the order in which the operations are performed in mathematical expressions. Lessons are included on numerical and variable expressions, as well as on writing, evaluating, and simplifying these expressions. These concepts are extended to polynomials, with lessons on simplifying, adding, subtracting, multiplying, dividing, and factoring polynomials. There are also lessons on more general formulas, including evaluating and rewriting formulas. On the following Topics slide there is a link to a table of contents for each topic. Clicking on a link on a Contents slide will take you to the first lesson slide for that topic. In many cases, there will be more than one slide on that topic. Work through as many as you need to master the topic, and then go on to the next topic. Clicking on the heading for a slide will take you back to the Contents slide for that topic; clicking on Return to Topics List on the Contents slide will take you back to the main Topics page.

4 Topics Sets of Real Numbers Properties of Operations Order of Operations Numerical Expressions Variables and Expressions Writing Variable Expressions Evaluating Variable Expressions Simplifying Variable Expressions Polynomial Expressions Polynomial Multiplication Polynomial Division Factoring Polynomials Formulas & Polynomials in Two (or more) Variables Polynomial Functions

5 Sets of Real Numbers Description and examples of subsets of the set of real numbers, including the rational numbers and irrational numbers Subsets of the Real Numbers Recognizing Irrational and Rational Numbers Interactive Practice Problems: Recognizing Rational and Irrational Numbers Interactive Practice Problems: Recognizing Rational and Irrational Numbers Return to Topics List CONTENTS:

6 Link: Number SetsNumber SetsLink: Number SetsNumber Sets Khan Academy video giving definitions of the various subsets of the real numbers Subsets include natural numbers, whole numbers, integers, rational numbers, and irrational numbers, with examples of numbers in each subset Time 5:17 Sets of Real Numbers

7 Link: Real NumbersReal NumbersLink: Real NumbersReal Numbers Mathispower4u video on sets of real numbers Describes various sets of real numbers, size comparison of real numbers, and absolute values Time 9:07 Sets of Real Numbers

8 Link: Recognizing Irrational NumbersRecognizing Irrational NumbersLink: Recognizing Irrational NumbersRecognizing Irrational Numbers Khan Academy video explaining the difference between rational and irrational numbers Time 2:18 Sets of Real Numbers

9 Link: Recognizing Rational and Irrational NumbersRecognizing Rational and Irrational NumbersLink: Recognizing Rational and Irrational NumbersRecognizing Rational and Irrational Numbers Khan Academy interactive practice problems on recognizing rational and irrational numbers A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Sets of Real Numbers

10 Properties of Operations Descriptions and examples of properties of operations on numbers, including commutative, associative, and distributive laws; identities and inverses for multiplication and addition Terminology of Properties of Numbers Commutative Property of Addition Commutative Property of Multiplication Associative Law of Addition Associative Law of Multiplication Identity Properties of 0 and 1 Inverse Properties of Addition and Multiplication The Distributive Property Interactive Practice Problems: Distributive Property Return to Topics List CONTENTS:

11 Link: Properties of Numbers 1Properties of Numbers 1Link: Properties of Numbers 1Properties of Numbers 1 Khan Academy video examples recognizing the associative and commutative properties of arithmetic Time 2:03 Properties of Operations

12 Link: Number Properties Terminology 1Number Properties Terminology 1Link: Number Properties Terminology 1Number Properties Terminology 1 Khan Academy video examples recognizing the distributive, associative, and commutative properties of arithmetic Time 3:05 Properties of Operations

13 Link: Properties of Numbers 2Properties of Numbers 2Link: Properties of Numbers 2Properties of Numbers 2 Khan Academy video examples recognizing the properties of arithmetic Time 1:52 Properties of Operations

14 Link: Commutative Law of AdditionCommutative Law of AdditionLink: Commutative Law of AdditionCommutative Law of Addition Khan Academy video example applying the commutative and associative laws of addition to rewrite a number expression Time 1:40 Properties of Operations

15 Link: Commutative Property for AdditionCommutative Property for AdditionLink: Commutative Property for AdditionCommutative Property for Addition Khan Academy video example applying the commutative and associative laws of addition to rewrite a number expression Time 3:23 Properties of Operations

16 Link: Commutative Property of MultiplicationCommutative Property of MultiplicationLink: Commutative Property of MultiplicationCommutative Property of Multiplication Khan Academy video example applying the commutative law of multiplication to rewrite a number expression Time 1:48 Properties of Operations

17 Link: Associative Law of AdditionAssociative Law of AdditionLink: Associative Law of AdditionAssociative Law of Addition Khan Academy video example applying the associative law of addition to rewrite a number expression Time 2:10 Properties of Operations

18 Link: Associative Law of MultiplicationAssociative Law of MultiplicationLink: Associative Law of MultiplicationAssociative Law of Multiplication Khan Academy video example applying the associative law of multiplication to rewrite a number expression Time 2:15 Properties of Operations

19 Link: Identity Property of 0Identity Property of 0Link: Identity Property of 0Identity Property of 0 Khan Academy video examples demonstrating the additive identity property of 0 Uses the method of the number line and absolute values when adding a zero in a numerical expression with more than one operation Time 4:46 Properties of Operations

20 Link: Identity Property of 1Identity Property of 1Link: Identity Property of 1Identity Property of 1 Khan Academy video examples demonstrating the multiplicative identity property of 1, explaining that you always get the original term number as the answer Time 1:24 Properties of Operations

21 Link: Identity Property of 1 (Second Example)Identity Property of 1 (Second Example)Link: Identity Property of 1 (Second Example)Identity Property of 1 (Second Example) Khan Academy video with more examples demonstrating the multiplicative identity property of 1 Time 1:55 Properties of Operations

22 Link: Inverse Property of AdditionInverse Property of AdditionLink: Inverse Property of AdditionInverse Property of Addition Khan Academy video examples of using the additive inverse to move from a given number back to zero The number line method is used to visualize the impact of adding the opposite of the given number Time 2:59 Properties of Operations

23 Link: Inverse Property of MultiplicationInverse Property of MultiplicationLink: Inverse Property of MultiplicationInverse Property of Multiplication Khan Academy video examples demonstrating the multiplicative inverse property Uses the operation of division and builds to multiplication by the reciprocal Time 3:16 Properties of Operations

24 Link: The Distributive PropertyThe Distributive PropertyLink: The Distributive PropertyThe Distributive Property Khan Academy video example demonstrating the distributive property of multiplication over addition, with an explanation of why the distributive property works Time 4:56 Properties of Operations

25 Link: The Distributive Property 2The Distributive Property 2Link: The Distributive Property 2The Distributive Property 2 Khan Academy video example demonstrating the distributive property of multiplication over subtraction Time 2:11 Properties of Operations

26 Link: The Distributive Property Example 1The Distributive Property Example 1Link: The Distributive Property Example 1The Distributive Property Example 1 Khan Academy video examples demonstrating the distributive property in several algebraic expressions Examples require combining like terms and distributing fractions Time 5:39 Properties of Operations

27 Link: Distributive Property ExerciseDistributive Property ExerciseLink: Distributive Property ExerciseDistributive Property Exercise Khan Academy video examples demonstrating the distributive property of multiplication over addition in numerical expressions One problem reviews factoring the greatest common divisor and writing a distributive expression Time 3:03 Properties of Operations

28 Link: The Distributive PropertyThe Distributive PropertyLink: The Distributive PropertyThe Distributive Property Math Planet text and video examples demonstrating the distributive property in several situations Time 1:41 Properties of Operations

29 Link: Distributive PropertyDistributive PropertyLink: Distributive PropertyDistributive Property Khan Academy interactive practice problems on the distributive property A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Properties of Operations

30 Order of Operations Descriptions and examples of the conventions on the order of operations in numerical and variable expressions Introduction to Order of Operations Order of Operations Examples Order of Operations With and Without Parentheses Interactive Practice Problems: Order of Operations Interactive Practice Problems: Expressions With Parentheses Return to Topics List CONTENTS:

31 Link: Introduction to Order of OperationsIntroduction to Order of OperationsLink: Introduction to Order of OperationsIntroduction to Order of Operations Khan Academy video introducing the order of operations on numbers Examples show the impact of the agreed upon order for simplifying numerical expressions Examples also explain operations at the same level and the left to right rule Time 9:40 Order of Operations

32 Link: The Order of OperationsThe Order of OperationsLink: The Order of OperationsThe Order of Operations Mathispower4u video introducing the order of operations on numbers Includes several examples applying the order of operations to simplify expressions Time 6:31 Order of Operations

33 Link: Order of OperationsOrder of OperationsLink: Order of OperationsOrder of Operations Khan Academy video example applying the order of operations on numbers to simplify a numerical expression Time 4:27 Order of Operations

34 Link: Order of Operations with ExponentsOrder of Operations with ExponentsLink: Order of Operations with ExponentsOrder of Operations with Exponents Khan Academy video example applying the order of operations on numbers Time 4:36 Order of Operations

35 Link: More Complicated Order of Operations ExampleMore Complicated Order of Operations ExampleLink: More Complicated Order of Operations ExampleMore Complicated Order of Operations Example Khan Academy video advanced example applying the order of operations to a numerical expression involving parentheses Time 5:20 Order of Operations

36 Link: Order of Operations ExamplesOrder of Operations ExamplesLink: Order of Operations ExamplesOrder of Operations Examples Khan Academy video advanced examples applying the order of operations on numbers Time 14:23 Order of Operations

37 Link: Evaluating an Expression With and Without ParenthesesEvaluating an Expression With and Without ParenthesesLink: Evaluating an Expression With and Without ParenthesesEvaluating an Expression With and Without Parentheses Khan Academy video example demonstrating the effect of parentheses on the order of operations of numbers Time 2:06 Order of Operations

38 Link: Order of OperationsOrder of OperationsLink: Order of OperationsOrder of Operations Khan Academy interactive practice problems on order of operations of numbers A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Order of Operations

39 Link: Order of Operations with Negative NumbersOrder of Operations with Negative NumbersLink: Order of Operations with Negative NumbersOrder of Operations with Negative Numbers Khan Academy interactive practice problems on order of operations of numbers A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Order of Operations

40 Link: Expressions With ParenthesesExpressions With ParenthesesLink: Expressions With ParenthesesExpressions With Parentheses Khan Academy interactive practice problems on evaluating numerical expressions containing parentheses A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Order of Operations

41 Numerical Expressions Examples and interactive problems on writing numerical expressions from verbal phrases Constructing Numerical Expressions Example Interactive Practice Problems: Writing Numerical Expressions Return to Topics List CONTENTS:

42 Link: Constructing Numerical Expressions ExampleConstructing Numerical Expressions ExampleLink: Constructing Numerical Expressions ExampleConstructing Numerical Expressions Example Khan Academy Video example constructing a numerical expression from a verbal phrase Time 1:22 Numerical Expressions

43 Link: Writing Numerical Expressions with ExponentsWriting Numerical Expressions with ExponentsLink: Writing Numerical Expressions with ExponentsWriting Numerical Expressions with Exponents Khan Academy interactive practice problems on writing numerical expressions from verbal phrases A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Numerical Expressions

44 Link: Writing Numerical Expressions with Exponents Word Problems Writing Numerical Expressions with Exponents Word Problems Link: Writing Numerical Expressions with Exponents Word Problems Writing Numerical Expressions with Exponents Word Problems Khan Academy interactive practice problems on writing numerical expressions with exponents from word problems A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Numerical Expressions

45 Variables and Expressions Description and examples of variables and expressions What is a Variable? Introduction to Variables and Expressions Notations for Multiplication With Variables Return to Topics List CONTENTS:

46 Link: What is a Variable?What is a Variable?Link: What is a Variable?What is a Variable? Khan Academy video example introducing the concept of a variable Time 3:18 Variables and Expressions

47 Link: Introduction to Variables and Variable ExpressionsIntroduction to Variables and Variable ExpressionsLink: Introduction to Variables and Variable ExpressionsIntroduction to Variables and Variable Expressions Mathispower4u video introducing and explaining the concepts of variables and variable expressions Also explains the difference between an expression and an equation Includes examples of writing variable expressions from verbal phrases evaluating a variable expression at a number Time 7:55 Variables and Expressions

48 Link: Why Aren't We Using the Multiplication Sign?Why Aren't We Using the Multiplication Sign?Link: Why Aren't We Using the Multiplication Sign?Why Aren't We Using the Multiplication Sign? Khan Academy video examples demonstrating the use of variables and various notation for multiplication with variables Time 4:58 Variables and Expressions

49 Writing Variable Expressions Translating verbal phrases into mathematical expressions Constructing Algebraic Expressions from Verbal Phrases Writing an Equation from a Word Problem Interactive Practice Problems: Writing Simple Variable Expressions Interactive Practice Problems: Writing Simple Variable Expressions Interactive Practice Problems: Writing Compound Variable Expressions Interactive Practice Problems: Writing Compound Variable Expressions Interactive Practice Problems: Writing Expressions from Word Problems Interactive Practice Problems: Writing Expressions from Word Problems Return to Topics List CONTENTS:

50 Link: How Do You Turn a Simple Verbal Phrase Into an Algebraic Expression? How Do You Turn a Simple Verbal Phrase Into an Algebraic Expression? Link: How Do You Turn a Simple Verbal Phrase Into an Algebraic Expression? How Do You Turn a Simple Verbal Phrase Into an Algebraic Expression? Virtual Nerd video introduction to translating verbal phrases into algebraic expressions Examples are given of very basic phrases that require each of the operations of addition, subtraction, multiplication, and division Translates words such as sum, total, difference, product, quotient, and ratio Time 3:36 Writing Variable Expressions

51 Link: How Do You Turn a Longer Verbal Phrase Into an Algebraic Expression? How Do You Turn a Longer Verbal Phrase Into an Algebraic Expression? Link: How Do You Turn a Longer Verbal Phrase Into an Algebraic Expression? How Do You Turn a Longer Verbal Phrase Into an Algebraic Expression? Virtual Nerd video example of translating a verbal phrase into an equation The example given is a compound phrase involving addition, multiplication, and fractions This example is also used in the video How Do You Write an Equation from a Word Problem?How Do You Write an Equation from a Word Problem? Time 5:10 Writing Variable Expressions

52 Link: Ex 1: Writing Basic Algebraic ExpressionsEx 1: Writing Basic Algebraic ExpressionsLink: Ex 1: Writing Basic Algebraic ExpressionsEx 1: Writing Basic Algebraic Expressions Mathispower4u video introduction to translating verbal phrases into algebraic expressions Examples are given of very basic phrases that require each of the operations of addition and subtraction Time 1:59 Writing Variable Expressions

53 Link: Ex 2: Writing Basic Algebraic ExpressionsEx 2: Writing Basic Algebraic ExpressionsLink: Ex 2: Writing Basic Algebraic ExpressionsEx 2: Writing Basic Algebraic Expressions Mathispower4u video example of translating a verbal phrase into an algebraic expression Example expresses the remaining part of a total distance in terms of the total and a given part of the total Time 2:35 Writing Variable Expressions

54 Link: Writing Expressions 1Writing Expressions 1Link: Writing Expressions 1Writing Expressions 1 Khan Academy video examples writing variable expressions from verbal phrases Vocabulary reviewed in the examples includes quantity, sum, and product translated into mathematical expressions Time 1:38 Writing Variable Expressions

55 Link: Writing Expressions 2Writing Expressions 2Link: Writing Expressions 2Writing Expressions 2 Khan Academy video examples writing variable expressions from verbal phrases Time 2:45 Writing Variable Expressions

56 Link: Writing Expressions 2 Exercise ExampleWriting Expressions 2 Exercise ExampleLink: Writing Expressions 2 Exercise ExampleWriting Expressions 2 Exercise Example Khan Academy video multiple choice example writing a variable expression from a verbal phrase Explains why some selections are incorrect and one is correct Time 2:23 Writing Variable Expressions

57 Link: Writing Expressions 3 Exercise Example 1Writing Expressions 3 Exercise Example 1Link: Writing Expressions 3 Exercise Example 1Writing Expressions 3 Exercise Example 1 Khan Academy video example writing an expression in two variables from a complex word problem Time 2:24 Writing Variable Expressions

58 Link: Writing Expressions 3 Exercise Example 2Writing Expressions 3 Exercise Example 2Link: Writing Expressions 3 Exercise Example 2Writing Expressions 3 Exercise Example 2 Khan Academy video example writing an expression in one variable from a verbal phrase Example involves a word problem about volumes of cubes Time 1:20 Writing Variable Expressions

59 Link: Writing Expressions 3 Exercise Example 3Writing Expressions 3 Exercise Example 3Link: Writing Expressions 3 Exercise Example 3Writing Expressions 3 Exercise Example 3 Khan Academy video example writing an expression in several variables from a verbal phrase Time 0:43 Writing Variable Expressions

60 Link: How Do You Write an Equation from a Word Problem?How Do You Write an Equation from a Word Problem?Link: How Do You Write an Equation from a Word Problem?How Do You Write an Equation from a Word Problem? Virtual Nerd video example of translating the phrases in a word problem into variables and an equation See also the video How Do You Turn a Longer Verbal Phrase Into an Algebraic Expression?How Do You Turn a Longer Verbal Phrase Into an Algebraic Expression? Time 4:00 Writing Variable Expressions

61 Link: Connect English with Mathematics and Graphing Lines (Part 1) Connect English with Mathematics and Graphing Lines (Part 1) Link: Connect English with Mathematics and Graphing Lines (Part 1) Connect English with Mathematics and Graphing Lines (Part 1) AlRichards314 video introduction to translating verbal phrases into algebraic expressions Examples are given of translating very basic phrases including phrases such as increased by and decreased by Also includes translation of a word problem into a system of two linear equations Time 5:19 Writing Variable Expressions

62 Link: Writing ExpressionsWriting ExpressionsLink: Writing ExpressionsWriting Expressions Khan Academy interactive practice problems on writing simple variable expressions from verbal phrases A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Writing Variable Expressions

63 Link: Writing Expressions 2Writing Expressions 2Link: Writing Expressions 2Writing Expressions 2 Khan Academy interactive practice problems on writing compound variable expressions from verbal phrases A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Writing Variable Expressions

64 Link: Writing Expressions with Variables Word ProblemsWriting Expressions with Variables Word ProblemsLink: Writing Expressions with Variables Word ProblemsWriting Expressions with Variables Word Problems Khan Academy interactive practice problems on writing variable expressions from word problems A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Writing Variable Expressions

65 Evaluating Variable Expressions Description and examples of evaluating variable expressions by substituting specific numbers for the variables Evaluating Algebraic Expressions Evaluating Expressions With Two Variables Evaluating Expressions Where Individual Variable Values are Unknown Evaluating Expressions Where Individual Variable Values are Unknown Evaluating Expressions in Word Problems Interactive Practice Problems: Evaluating Expressions in One Variable Interactive Practice Problems: Evaluating Expressions in One Variable Interactive Practice Problems: Evaluating Expressions in Two Variables Interactive Practice Problems: Evaluating Expressions in Two Variables Interactive Practice Problems: Evaluating Expressions With Variables in Word Problems Interactive Practice Problems: Evaluating Expressions With Variables in Word Problems Return to Topics List CONTENTS:

66 Link: Evaluating Algebraic ExpressionsEvaluating Algebraic ExpressionsLink: Evaluating Algebraic ExpressionsEvaluating Algebraic Expressions Mathispower4u video examples introducing evaluating various types of algebraic expressions at specific numbers Defines variable expressions and reviews order of operations Steps use substitution, order of operations, exponents, and fractions Time 7:52 Evaluating Variable Expressions

67 Link: Evaluating Expressions With One VariableEvaluating Expressions With One VariableLink: Evaluating Expressions With One VariableEvaluating Expressions With One Variable Khan Academy video of very basic examples of evaluating algebraic expressions at specific numbers Time 3:21 Evaluating Variable Expressions

68 Link: Example: Evaluating an ExpressionExample: Evaluating an ExpressionLink: Example: Evaluating an ExpressionExample: Evaluating an Expression Khan Academy video example of evaluating an algebraic expression at specific numbers Time 2:00 Evaluating Variable Expressions

69 Link: Expressions With Two VariablesExpressions With Two VariablesLink: Expressions With Two VariablesExpressions With Two Variables Khan Academy video examples introducing evaluating expressions in two variables Time 1:58 Evaluating Variable Expressions

70 Link: Example: Evaluating Expressions With 2 VariablesExample: Evaluating Expressions With 2 VariablesLink: Example: Evaluating Expressions With 2 VariablesExample: Evaluating Expressions With 2 Variables Khan Academy video example of evaluating an algebraic expression with two variables at specific numbers Time 1:46 Evaluating Variable Expressions

71 Link: Ex: Evaluate a Variable Expression with Exponents and Fractions Ex: Evaluate a Variable Expression with Exponents and Fractions Link: Ex: Evaluate a Variable Expression with Exponents and Fractions Ex: Evaluate a Variable Expression with Exponents and Fractions Mathispower4u video example of substituting values into an expression with exponents and fractions Reviews order of operations 2:33 Evaluating Variable Expressions

72 Link: Examples of Evaluating Variable ExpressionsExamples of Evaluating Variable ExpressionsLink: Examples of Evaluating Variable ExpressionsExamples of Evaluating Variable Expressions Khan Academy video examples of evaluating algebraic expressions of many types Time 12:26 Evaluating Variable Expressions

73 Link: Evaluating Expressions Where Individual Variable Values are Unknown Evaluating Expressions Where Individual Variable Values are Unknown Link: Evaluating Expressions Where Individual Variable Values are Unknown Evaluating Expressions Where Individual Variable Values are Unknown Khan Academy video examples of evaluating variable expressions where relationships between the variables are known but individual variable values are not 4:39 Evaluating Variable Expressions

74 Link: Evaluating Expressions with Unknown Variables 2Evaluating Expressions with Unknown Variables 2Link: Evaluating Expressions with Unknown Variables 2Evaluating Expressions with Unknown Variables 2 Khan Academy video examples of evaluating variable expressions where relationships between the variables are known but individual variable values are not 3:00 Evaluating Variable Expressions

75 Link: Example Evaluating Expressions in Word ProblemsExample Evaluating Expressions in Word ProblemsLink: Example Evaluating Expressions in Word ProblemsExample Evaluating Expressions in Word Problems Khan Academy video example of evaluating an algebraic expression in a word problem Time 3:24 Evaluating Variable Expressions

76 Link: Evaluating Expressions in One VariableEvaluating Expressions in One VariableLink: Evaluating Expressions in One VariableEvaluating Expressions in One Variable Khan Academy interactive practice problems on evaluating algebraic expressions in one variable A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Evaluating Variable Expressions

77 Link: Evaluating Expressions in Two VariablesEvaluating Expressions in Two VariablesLink: Evaluating Expressions in Two VariablesEvaluating Expressions in Two Variables Khan Academy interactive practice problems on evaluating algebraic expressions in two variables A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Evaluating Variable Expressions

78 Link: Evaluating Expressions With Variables in Word ProblemsEvaluating Expressions With Variables in Word ProblemsLink: Evaluating Expressions With Variables in Word ProblemsEvaluating Expressions With Variables in Word Problems Khan Academy interactive practice problems on evaluating algebraic expressions in word problems A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Evaluating Variable Expressions

79 Simplifying Variable Expressions Description and examples of using properties of operations and combining like terms to simplify variable expressions Combining Like Terms Equivalent Forms of Expressions Interactive Practice Problems: Equivalent Forms of Expressions Return to Topics List CONTENTS:

80 Link: Combining Like TermsCombining Like TermsLink: Combining Like TermsCombining Like Terms Khan Academy video explaining like terms and how to combine like terms 4:32 Simplifying Variable Expressions

81 Link: Adding Like Rational TermsAdding Like Rational TermsLink: Adding Like Rational TermsAdding Like Rational Terms Khan Academy video example of combining two variable expressions with fractions 1:14 Simplifying Variable Expressions

82 Link: Combining Like Terms 1Combining Like Terms 1Link: Combining Like Terms 1Combining Like Terms 1 Khan Academy video example of combining like terms to simplify an algebraic expression 3:06 Simplifying Variable Expressions

83 Link: Combining Like Terms 2Combining Like Terms 2Link: Combining Like Terms 2Combining Like Terms 2 Khan Academy video example of combining like terms to simplify a complex variable expression Reviews commutative property of addition to group like terms by changing the order 3:43 Simplifying Variable Expressions

84 Link: Equivalent Forms of Expressions 1Equivalent Forms of Expressions 1Link: Equivalent Forms of Expressions 1Equivalent Forms of Expressions 1 Khan Academy video with multiple choice examples using properties of operations to find simpler equivalent forms of algebraic expressions Reviews the distributive and commutative properties and explains why some of the expressions are not equivalent 5:32 Simplifying Variable Expressions

85 Link: Equivalent Forms of Expressions 1Equivalent Forms of Expressions 1Link: Equivalent Forms of Expressions 1Equivalent Forms of Expressions 1 Khan Academy interactive practice problems on simplifying algebraic expressions using distributive and commutative properties and combining like terms A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Simplifying Variable Expressions

86 Polynomial Expressions Introduction to polynomial expressions, including terminology, simplifying, adding and subtracting Definitions and Terminology Combining Like Terms to Simplify Polynomials Adding and Subtracting Polynomials Interactive Practice Problems: Adding and Subtracting Polynomials Interactive Practice Problems: Adding and Subtracting Polynomials Operations with Polynomials Calculator Return to Topics List CONTENTS:

87 Link: Polynomials: Definitions / EvaluationPolynomials: Definitions / EvaluationLink: Polynomials: Definitions / EvaluationPolynomials: Definitions / Evaluation Purplemath text lesson on the terminology of polynomials Includes definitions of term, degree, coefficient, constant term, leading term, polynomial, and monomial Also introduces evaluation of a polynomial at a specific number simplifying by combining like terms Polynomial Expressions

88 Link: Polynomial Expressions 1 - Explaining Polynomial Expressions Polynomial Expressions 1 - Explaining Polynomial Expressions Link: Polynomial Expressions 1 - Explaining Polynomial Expressions Polynomial Expressions 1 - Explaining Polynomial Expressions Tutortag video introducing the terminology of polynomials Includes definitions of coefficient, polynomial, monomial, binomial, and trinomial Time 2:43 Polynomial Expressions

89 Link: Terms, Coefficients, and Exponents in a PolynomialTerms, Coefficients, and Exponents in a PolynomialLink: Terms, Coefficients, and Exponents in a PolynomialTerms, Coefficients, and Exponents in a Polynomial Khan Academy video introducing the terminology of polynomials via an example Includes identification of terms, coefficients, and exponents Time 2:36 Polynomial Expressions

90 Link: Ex: Intro to Polynomials in One VariableEx: Intro to Polynomials in One VariableLink: Ex: Intro to Polynomials in One VariableEx: Intro to Polynomials in One Variable Mathispower4u video introducing the terminology of polynomials via an example Includes definition of polynomial and identification of terms, degrees, coefficients, leading term, and the degree of a polynomial Time 2:59 Polynomial Expressions

91 Link: Combining Like TermsCombining Like TermsLink: Combining Like TermsCombining Like Terms Mathispower4u video introducing like terms and simplifying polynomials by combining like terms Includes definition of like terms and examples of like terms and unlike terms Discusses the distributive law and its role in combining like terms, as well as how combining like terms is done in practice Includes examples of simplifying polynomials in one or two variables Time 4:49 Polynomial Expressions

92 Link: Simply a PolynomialSimply a PolynomialLink: Simply a PolynomialSimply a Polynomial Khan Academy video example of simplifying a polynomial by combining like terms Explains the difference between like and unlike terms Time 3:37 Polynomial Expressions

93 Link: Addition and Subtraction of PolynomialsAddition and Subtraction of PolynomialsLink: Addition and Subtraction of PolynomialsAddition and Subtraction of Polynomials Khan Academy video introducing addition and subtraction of polynomials by combining like terms Includes an explanation of what a polynomial is, plus terminology such as term, constant term, degree, coefficient, and standard form Examples include addition of polynomials in one variable by combining like terms subtraction of polynomials in two variables by first distributing the minus sign and then combining like terms constructing polynomials representing areas of figures Time 15:59 Polynomial Expressions

94 Link: Simplifying Algebraic ExpressionsSimplifying Algebraic ExpressionsLink: Simplifying Algebraic ExpressionsSimplifying Algebraic Expressions Mathispower4u video introducing using the distributive property to clear parentheses and combining like terms in polynomial expressions Reviews the distributive property Reviews multiplicative property of -1 (i.e., -1a = -a) and the opposite of a sum (i.e., distributing a minus sign across a sum) Includes examples of simplifying expressions Time 5:24 Polynomial Expressions

95 Link: Simplify Polynomial Expressions - Add/Subtract/Multiply Simplify Polynomial Expressions - Add/Subtract/Multiply Link: Simplify Polynomial Expressions - Add/Subtract/Multiply Simplify Polynomial Expressions - Add/Subtract/Multiply Mathispower4u video examples of simplifying polynomials Examples include adding and subtracting polynomials by clearing parentheses and combining like terms distributing a constant across a sum to clear parentheses distributing a non-constant monomial across a sum Time 4:22 Polynomial Expressions

96 Link: Adding and Subtracting PolynomialsAdding and Subtracting PolynomialsLink: Adding and Subtracting PolynomialsAdding and Subtracting Polynomials Purplemath text lesson on adding and subtracting polynomials Includes examples of adding polynomials (both horizontally and vertically) by clearing parentheses and combining like terms subtracting polynomials (both horizontally and vertically) by distributing the minus sign (or -1) across a sum to clear parentheses and then combining like terms Polynomial Expressions

97 Link: How Do You Add Polynomials?How Do You Add Polynomials?Link: How Do You Add Polynomials?How Do You Add Polynomials? Virtual Nerd video example of adding polynomials Gives step-by-step instructions to rewrite the sum without parentheses identify the like terms group like terms combine like terms rewrite the sum in standard form Time 4:59 Polynomial Expressions

98 Link: Adding PolynomialsAdding PolynomialsLink: Adding PolynomialsAdding Polynomials Mathispower4u video examples of adding polynomials by clearing parentheses and combining like terms Time 5:09 Polynomial Expressions

99 Link: How Do You Subtract Polynomials?How Do You Subtract Polynomials?Link: How Do You Subtract Polynomials?How Do You Subtract Polynomials? Virtual Nerd video example of subtracting polynomials Gives step-by-step instructions to distribute the minus sign to remove parentheses identify the like terms group like terms combine like terms Time 2:07 Polynomial Expressions

100 Link: Subtracting PolynomialsSubtracting PolynomialsLink: Subtracting PolynomialsSubtracting Polynomials Mathispower4u video examples of subtracting polynomials by distributing a -1 to clear parentheses and combining like terms Time 4:43 Polynomial Expressions

101 Link: Adding and Subtracting Polynomials 1Adding and Subtracting Polynomials 1Link: Adding and Subtracting Polynomials 1Adding and Subtracting Polynomials 1 Khan Academy video example of adding polynomials by clearing parentheses and combining like terms Time 2:01 Polynomial Expressions

102 Link: Adding and Subtracting Polynomials 2Adding and Subtracting Polynomials 2Link: Adding and Subtracting Polynomials 2Adding and Subtracting Polynomials 2 Khan Academy video example of subtracting polynomials by distributing a -1 to clear parentheses and combining like terms Time 1:43 Polynomial Expressions

103 Link: Adding and Subtracting Polynomials 3Adding and Subtracting Polynomials 3Link: Adding and Subtracting Polynomials 3Adding and Subtracting Polynomials 3 Khan Academy video example of adding and subtracting polynomials in one expression by clearing parentheses and combining like terms Time 2:27 Polynomial Expressions

104 Link: Practice Adding/Subtracting PolynomialsPractice Adding/Subtracting PolynomialsLink: Practice Adding/Subtracting PolynomialsPractice Adding/Subtracting Polynomials Khan Academy interactive practice problems on simplifying sums and differences of polynomials A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Polynomial Expressions

105 Link: Operations with Polynomials CalculatorOperations with Polynomials CalculatorLink: Operations with Polynomials CalculatorOperations with Polynomials Calculator Math Portal polynomial operation calculator Enter two polynomials and the calculator will add, subtract, multiply, or divide the polynomials as requested Calculator can also generate examples A complete step-by-step solution is given if requested Polynomial Expressions

106 Polynomial Multiplication Description and examples of multiplying polynomials, including special products Multiplying Monomials Multiplying Monomials by Polynomials Multiplying Binomials; FOIL Method Special Products of Binomials: Squares and Conjugates Multiplying a Binomial and a Trinomial General Multiplication of Polynomials Interactive Practice Problems: Multiplying Simple Polynomials Interactive Practice Problems: Multiplying General Polynomials Operations with Polynomials Calculator Return to Topics List CONTENTS:

107 Link: Multiplying MonomialsMultiplying MonomialsLink: Multiplying MonomialsMultiplying Monomials Mathispower4u video examples of multiplying monomials and raising a monomial to a power using the laws of exponents Time 2:53 Polynomial Multiplication

108 Link: How Do You Multiply Monomials?How Do You Multiply Monomials?Link: How Do You Multiply Monomials?How Do You Multiply Monomials? Virtual Nerd video example simplifying a product of three monomials in two variables by regrouping the factors and using laws of exponents Time 1:20 Polynomial Multiplication

109 Link: Multiplying Monomials by PolynomialsMultiplying Monomials by PolynomialsLink: Multiplying Monomials by PolynomialsMultiplying Monomials by Polynomials Khan Academy video example of multiplying a monomial by a trinomial, using the distributive property and laws of exponents Time 2:43 Polynomial Multiplication

110 Link: How Do You Multiply a Monomial by a Polynomial?How Do You Multiply a Monomial by a Polynomial?Link: How Do You Multiply a Monomial by a Polynomial?How Do You Multiply a Monomial by a Polynomial? Virtual Nerd video example of multiplying a monomial by a trinomial in two variables, using the distributive property and laws of exponents Time 1:27 Polynomial Multiplication

111 Link: Ex: Multiplying Using the Distributive PropertyEx: Multiplying Using the Distributive PropertyLink: Ex: Multiplying Using the Distributive PropertyEx: Multiplying Using the Distributive Property Mathispower4u video examples of multiplying monomials by polynomials, using the distributive property and laws of exponents Time 2:54 Polynomial Multiplication

112 Link: Simple Polynomial MultiplicationSimple Polynomial MultiplicationLink: Simple Polynomial MultiplicationSimple Polynomial Multiplication Purplemath text lesson introducing multiplication of polynomials Topics and examples include multiplication of monomials using laws of exponents multiplication of a monomial by a polynomial using the distributive law and laws of exponents multiplication of two binomials horizontally using the distributive law, vertically, and using the FOIL method multiplication of polynomials with more than two terms horizontally and vertically Polynomial Multiplication

113 Link: FOIL for Multiplying BinomialsFOIL for Multiplying BinomialsLink: FOIL for Multiplying BinomialsFOIL for Multiplying Binomials Khan Academy video example of multiplying two binomials, first using the FOIL method and then using the distributive law twice Time 5:47 Polynomial Multiplication

114 Link: Multiplying BinomialsMultiplying BinomialsLink: Multiplying BinomialsMultiplying Binomials Mathispower4u video examples of multiplying two binomials using the distributive property and the FOIL method Time 4:12 Polynomial Multiplication

115 Link: Special Products of BinomialsSpecial Products of BinomialsLink: Special Products of BinomialsSpecial Products of Binomials Khan Academy video on squaring binomials and the product of a sum and a difference of two terms Topics include both specific examples and general formulas for the square of a binomial the product of the sum of two terms and the difference of the same two terms Time 10:36 Polynomial Multiplication

116 Link: Ex: Squaring BinomialsEx: Squaring BinomialsLink: Ex: Squaring BinomialsEx: Squaring Binomials Mathispower4u video examples of squaring binomials by using the standard methods for multiplying binomials Also introduces formulas for squaring binomials without examples Time 3:22 Polynomial Multiplication

117 Link: Ex: Multiplying Binomial Conjugates - Special Binomial Products Ex: Multiplying Binomial Conjugates - Special Binomial Products Link: Ex: Multiplying Binomial Conjugates - Special Binomial Products Ex: Multiplying Binomial Conjugates - Special Binomial Products Mathispower4u video examples of the product of the sum of two terms and the difference of the same two terms using the standard methods for multiplying binomials Also defines conjugates and introduces the formula for a product of conjugates without examples Time 2:54 Polynomial Multiplication

118 Link: Special Products of Polynomials 1Special Products of Polynomials 1Link: Special Products of Polynomials 1Special Products of Polynomials 1 Khan Academy video on the product of the sum of two terms and the difference of the same two terms Derives and explains a general formula for such a product Includes an example using the formula Time 2:29 Polynomial Multiplication

119 Link: Ex: Polynomial Multiplication Involving Binomials and Trinomials Ex: Polynomial Multiplication Involving Binomials and Trinomials Link: Ex: Polynomial Multiplication Involving Binomials and Trinomials Ex: Polynomial Multiplication Involving Binomials and Trinomials Mathispower4u video examples of multiplying polynomials Examples are product of three factors: a monomial and two binomials product of a binomial and a trinomial Time 3:35 Polynomial Multiplication

120 Link: Multiplying PolynomialsMultiplying PolynomialsLink: Multiplying PolynomialsMultiplying Polynomials Khan Academy video example multiplying a binomial by trinomial first horizontally using the distributive law twice, and then vertically Time 5:46 Polynomial Multiplication

121 Link: More Multiplying PolynomialsMore Multiplying PolynomialsLink: More Multiplying PolynomialsMore Multiplying Polynomials Khan Academy video example multiplying a binomial by trinomial using the distributive law twice Time 2:34 Polynomial Multiplication

122 Link: Multiplying Polynomials 3Multiplying Polynomials 3Link: Multiplying Polynomials 3Multiplying Polynomials 3 Khan Academy video example multiplying a binomial by trinomial using the distributive law twice The product of the polynomials is introduced as representing a volume Time 4:19 Polynomial Multiplication

123 Link: Multiplication of PolynomialsMultiplication of PolynomialsLink: Multiplication of PolynomialsMultiplication of Polynomials Khan Academy video examples of multiplying various types of polynomials Types of examples include monomial times polynomial binomial times binomial binomial times trinomial, multiplied vertically Time 9:49 Polynomial Multiplication

124 Link: Multiplying Polynomials 1Multiplying Polynomials 1Link: Multiplying Polynomials 1Multiplying Polynomials 1 Khan Academy interactive practice problems on multiplying simple polynomials A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Polynomial Multiplication

125 Link: Multiplying Polynomials 2Multiplying Polynomials 2Link: Multiplying Polynomials 2Multiplying Polynomials 2 Khan Academy interactive practice problems on multiplying more complicated polynomials A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Polynomial Multiplication

126 Link: Operations with Polynomials CalculatorOperations with Polynomials CalculatorLink: Operations with Polynomials CalculatorOperations with Polynomials Calculator Math Portal polynomial operation calculator Enter two polynomials and the calculator will add, subtract, multiply, or divide the polynomials as requested Calculator can also generate examples A complete step-by-step solution is given if requested Polynomial Multiplication

127 Polynomial Division Description and examples of dividing polynomials, including long division and synthetic division Polynomial Divided by a Monomial Long Division of Polynomials Synthetic Division Operations with Polynomials Calculator Return to Topics List CONTENTS:

128 Link: Polynomial Divided by a MonomialPolynomial Divided by a MonomialLink: Polynomial Divided by a MonomialPolynomial Divided by a Monomial Khan Academy video example dividing a polynomial by a monomial using the distributive property and laws of exponents Time 4:44 Polynomial Division

129 Link: Ex: Divide a Polynomial by a MonomialEx: Divide a Polynomial by a MonomialLink: Ex: Divide a Polynomial by a MonomialEx: Divide a Polynomial by a Monomial Mathispower4u video examples dividing a polynomial by a monomial using the distributive property and laws of exponents Time 2:43 Polynomial Division

130 Link: Polynomial DivisionPolynomial DivisionLink: Polynomial DivisionPolynomial Division Purplemath text lesson on dividing polynomials Topics and examples include Dividing a polynomial by a monomial Factoring and cancelling (reducing a fraction) Long division, with and without a remainder Polynomial Division

131 Link: Polynomial Division: Long DivisionPolynomial Division: Long DivisionLink: Polynomial Division: Long DivisionPolynomial Division: Long Division Mathispower4u video of long division of a polynomial by a binomial Includes review of long division of numbers written procedure for long division of polynomials explained with an example further examples dividing a polynomial by a binomial Time 9:25 Polynomial Division

132 Link: Polynomial DivisionPolynomial DivisionLink: Polynomial DivisionPolynomial Division Khan Academy video examples of long division of polynomials with remainders Time 12:09 Polynomial Division

133 Link: Algebraic Long DivisionAlgebraic Long DivisionLink: Algebraic Long DivisionAlgebraic Long Division Khan Academy video with a (long) example of long division of polynomials Time 10:21 Polynomial Division

134 Link: How to do Long Division with PolynomialsHow to do Long Division with PolynomialsLink: How to do Long Division with PolynomialsHow to do Long Division with Polynomials Mathbff video examples of long division of polynomials with remainders Includes polynomials with missing terms Time 11:13 Polynomial Division

135 Link: Divide a Polynomial by a Degree Two BinomialDivide a Polynomial by a Degree Two BinomialLink: Divide a Polynomial by a Degree Two BinomialDivide a Polynomial by a Degree Two Binomial Mathispower4u video example of long division of a polynomial by a degree two binomial with a remainder Time 4:14 Polynomial Division

136 Link: Dividing Polynomials with RemaindersDividing Polynomials with RemaindersLink: Dividing Polynomials with RemaindersDividing Polynomials with Remainders Khan Academy video example of long division of polynomials with a remainder Includes a dividend with a missing term (i.e., 0 coefficient) Includes checking the answer by multiplying and simplifying Time 6:23 Polynomial Division

137 Link: Polynomial Division: Synthetic DivisionPolynomial Division: Synthetic DivisionLink: Polynomial Division: Synthetic DivisionPolynomial Division: Synthetic Division Mathispower4u video introducing synthetic division of a polynomial by a binomial of the form x – k Includes general explanation of the method of synthetic division several explicit examples example where the coefficient of x in the divisor is not 1 Time 10:07 Polynomial Division

138 Link: Synthetic DivisionSynthetic DivisionLink: Synthetic DivisionSynthetic Division Khan Academy video explaining synthetic division of a polynomial by a binomial of the form x + k via an example Time 5:21 Polynomial Division

139 Link: How to Do Synthetic DivisionHow to Do Synthetic DivisionLink: How to Do Synthetic DivisionHow to Do Synthetic Division Mathbff video explaining synthetic division of a polynomial by a binomial of the form x - k via an example Time 6:35 Polynomial Division

140 Link: Synthetic Division, Example 2Synthetic Division, Example 2Link: Synthetic Division, Example 2Synthetic Division, Example 2 Khan Academy video example of synthetic division of a polynomial by a binomial of the form x - k Includes a dividend with a missing term (i.e., 0 coefficient) Time 5:00 Polynomial Division

141 Link: Ex 2: Divide a Polynomial by a Binomial Using Synthetic Division Ex 2: Divide a Polynomial by a Binomial Using Synthetic Division Link: Ex 2: Divide a Polynomial by a Binomial Using Synthetic Division Ex 2: Divide a Polynomial by a Binomial Using Synthetic Division Mathispower4u video example of synthetic division of a polynomial by a binomial of the form x + k Time 3:22 Polynomial Division

142 Link: Ex 3: Divide a Polynomial by a Binomial Using Synthetic Division Ex 3: Divide a Polynomial by a Binomial Using Synthetic Division Link: Ex 3: Divide a Polynomial by a Binomial Using Synthetic Division Ex 3: Divide a Polynomial by a Binomial Using Synthetic Division Mathispower4u video example of synthetic division of a polynomial by a binomial of the form x - k Includes a dividend with a missing term (i.e., 0 coefficient) Time 3:13 Polynomial Division

143 Link: Ex 4: Divide a Polynomial by a Binomial Using Synthetic Division Ex 4: Divide a Polynomial by a Binomial Using Synthetic Division Link: Ex 4: Divide a Polynomial by a Binomial Using Synthetic Division Ex 4: Divide a Polynomial by a Binomial Using Synthetic Division Mathispower4u video example of synthetic division of a polynomial by a binomial of the form x + k Includes a dividend with a missing term (i.e., 0 coefficient) Time 3:17 Polynomial Division

144 Link: Operations with Polynomials CalculatorOperations with Polynomials CalculatorLink: Operations with Polynomials CalculatorOperations with Polynomials Calculator Math Portal polynomial operation calculator Enter two polynomials and the calculator will add, subtract, multiply, or divide the polynomials as requested Calculator can also generate examples A complete step-by-step solution is given if requested Polynomial Division

145 Factoring Polynomials Description and examples of factoring polynomials, including special forms and factoring by grouping Greatest Common Factor of Monomials Factoring the GCF of Terms Out of a Polynomial Factoring a Difference of Squares Factoring a Sum or Difference of Cubes Factoring Perfect Square Trinomials Factoring Quadratic Polynomials and Trinomials Interactive Practice Problems: Factoring Quadratics with Leading Coefficient 1 Interactive Practice Problems: Factoring Quadratics with Leading Coefficient 1 Interactive Practice Problems: Factoring Quadratics with Leading Coefficient Not 1 Interactive Practice Problems: Factoring Quadratics with Leading Coefficient Not 1 Factoring by Grouping Interactive Practice Problems: Factoring by Grouping Return to Topics List CONTENTS:

146 Link: How Do You Find the Greatest Common Factor of Monomials? How Do You Find the Greatest Common Factor of Monomials? Link: How Do You Find the Greatest Common Factor of Monomials? How Do You Find the Greatest Common Factor of Monomials? Virtual Nerd video example finding the greatest common factor of 4 monomials in 2 variables Steps used in the example to find the GCF are factor each monomial identify common factors list the common factors multiply the common factors Time 3:52 Factoring Polynomials

147 Link: Monomial Greatest Common FactorMonomial Greatest Common FactorLink: Monomial Greatest Common FactorMonomial Greatest Common Factor Khan Academy video example finding the greatest common factor of 2 monomials in 2 variables Time 3:13 Factoring Polynomials

148 Link: Factor Expressions Using the GCFFactor Expressions Using the GCFLink: Factor Expressions Using the GCFFactor Expressions Using the GCF Khan Academy video example of factoring the greatest common factor of the terms out of a binomial in two variables Begins with a review of finding the GCF of two monomials Time 5:28 Factoring Polynomials

149 Link: Ex 1: Identify GCF and Factor a BinomialEx 1: Identify GCF and Factor a BinomialLink: Ex 1: Identify GCF and Factor a BinomialEx 1: Identify GCF and Factor a Binomial Mathispower4u video examples of factoring the greatest common factor of the terms out of binomials Includes finding the GCF of the terms Time 4:16 Factoring Polynomials

150 Link: Ex 2: Identify GCF and Factor a TrinomialEx 2: Identify GCF and Factor a TrinomialLink: Ex 2: Identify GCF and Factor a TrinomialEx 2: Identify GCF and Factor a Trinomial Mathispower4u video examples of factoring the greatest common factor of the terms out of trinomials Includes finding the GCF of the terms Time 6:40 Factoring Polynomials

151 Link: How Do You Factor the Greatest Common Factor Out of a Polynomial? How Do You Factor the Greatest Common Factor Out of a Polynomial? Link: How Do You Factor the Greatest Common Factor Out of a Polynomial? How Do You Factor the Greatest Common Factor Out of a Polynomial? Virtual Nerd video example of factoring the greatest common factor of the terms out of a polynomial in two variables Includes finding the GCF of the terms Time 4:19 Factoring Polynomials

152 Link: Simple Polynomial FactoringSimple Polynomial FactoringLink: Simple Polynomial FactoringSimple Polynomial Factoring Purplemath text lesson on basic polynomial factoring techniques Topics and examples include factoring out the greatest common factor of the terms factoring by grouping (referred to here as factoring in pairs) for quadratics Factoring Polynomials

153 Link: How Do You Know if You Have a Difference of Squares?How Do You Know if You Have a Difference of Squares?Link: How Do You Know if You Have a Difference of Squares?How Do You Know if You Have a Difference of Squares? Virtual Nerd video explaining how to identify a binomial as a difference of squares Two issues to be aware of: considers only binomials with perfect square coefficients the condition the degree of each term must be even or 0 is true but slightly misleading, since 0 is even Time 2:26 Factoring Polynomials

154 Link: How Do You Factor a Polynomial Using Difference of Squares? How Do You Factor a Polynomial Using Difference of Squares? Link: How Do You Factor a Polynomial Using Difference of Squares? How Do You Factor a Polynomial Using Difference of Squares? Virtual Nerd video example giving a step-by-step procedure to factor a binomial that is a difference of squares Time 4:45 Factoring Polynomials

155 Link: Factoring a Difference of SquaresFactoring a Difference of SquaresLink: Factoring a Difference of SquaresFactoring a Difference of Squares Mathispower4u video introducing the factoring of a difference of squares Video includes identifying a difference of squares general formula for the factors of a difference of squares numerous examples from very basic to somewhat more advanced Time 5:25 Factoring Polynomials

156 Link: Example: Factor a Difference of SquaresExample: Factor a Difference of SquaresLink: Example: Factor a Difference of SquaresExample: Factor a Difference of Squares Mathispower4u video examples of factoring difference of squares binomials Includes review of the formula for the factors of a difference of squares and several examples Time 4:19 Factoring Polynomials

157 Link: Ex: Factor a Difference of Squares with a Common FactorEx: Factor a Difference of Squares with a Common FactorLink: Ex: Factor a Difference of Squares with a Common FactorEx: Factor a Difference of Squares with a Common Factor Mathispower4u video example of factoring a difference of squares binomial in which the terms have a (perfect square) common factor Time 3:06 Factoring Polynomials

158 Link: Factoring a Sum or Difference of CubesFactoring a Sum or Difference of CubesLink: Factoring a Sum or Difference of CubesFactoring a Sum or Difference of Cubes Mathispower4u video introducing factoring of sum of cubes and difference of cubes binomials Video includes general formulas for factors of sum and difference of cubes binomials verification of sum of cubes formula using long division examples, including one in which the terms of the binomial have a common factor Time 6:07 Factoring Polynomials

159 Link: How Do You Factor a Polynomial Using a Sum of Cubes?How Do You Factor a Polynomial Using a Sum of Cubes?Link: How Do You Factor a Polynomial Using a Sum of Cubes?How Do You Factor a Polynomial Using a Sum of Cubes? Virtual Nerd video example giving a step-by-step procedure for factoring a sum of cubes binomial Time 4:15 Factoring Polynomials

160 Link: How Do You Factor a Polynomial Using a Difference of Cubes? How Do You Factor a Polynomial Using a Difference of Cubes? Link: How Do You Factor a Polynomial Using a Difference of Cubes? How Do You Factor a Polynomial Using a Difference of Cubes? Virtual Nerd video example giving a step-by-step procedure for factoring a difference of cubes binomial Time 4:40 Factoring Polynomials

161 Link: Ex 1: Factor a Sum or Difference of CubesEx 1: Factor a Sum or Difference of CubesLink: Ex 1: Factor a Sum or Difference of CubesEx 1: Factor a Sum or Difference of Cubes Mathispower4u video examples of factoring a sum of cubes binomial and a difference of cubes binomial Video includes brief review of formulas for factors of sum and difference of cubes a basic example of each type Time 3:19 Factoring Polynomials

162 Link: Ex 2: Factor a Sum or Difference of CubesEx 2: Factor a Sum or Difference of CubesLink: Ex 2: Factor a Sum or Difference of CubesEx 2: Factor a Sum or Difference of Cubes Mathispower4u video examples of factoring a sum of cubes binomial and a difference of cubes binomial Video includes brief review of formulas for factors of sum and difference of cubes an example of each type in which the terms of the binomial have a common factor Time 3:35 Factoring Polynomials

163 Link: Ex 3: Factor a Sum or Difference of CubesEx 3: Factor a Sum or Difference of CubesLink: Ex 3: Factor a Sum or Difference of CubesEx 3: Factor a Sum or Difference of Cubes Mathispower4u video example of factoring a sum of cubes binomial Video includes brief review of formulas for factors of sum and difference of cubes an example of a sum of cubes in which the terms of the binomial have a perfect cube common factor and relatively large coefficients Time 5:23 Factoring Polynomials

164 Link: Factoring Perfect Square Trinomials & the Difference of Two Squares Factoring Perfect Square Trinomials & the Difference of Two Squares Link: Factoring Perfect Square Trinomials & the Difference of Two Squares Factoring Perfect Square Trinomials & the Difference of Two Squares AlRichards314 video on factoring trinomials that are squares of binomials and factoring difference of squares binomials Video includes review of formulas for the square of a binomial and the product of a sum of two terms and the difference of the same terms product formulas reinterpreted as factoring formulas several examples of each type Time 7:45 Factoring Polynomials

165 Link: Factoring a Perfect Square TrinomialFactoring a Perfect Square TrinomialLink: Factoring a Perfect Square TrinomialFactoring a Perfect Square Trinomial Mathispower4u video on factoring trinomials that are squares of binomials Video includes how to recognize a perfect square trinomial formula for the factors of a perfect square trinomial several examples, including one in which the terms of the trinomial have a common factor Time 7:52 Factoring Polynomials

166 Link: How Do You Use a Shortcut to Factor a Perfect Square Trinomial? How Do You Use a Shortcut to Factor a Perfect Square Trinomial? Link: How Do You Use a Shortcut to Factor a Perfect Square Trinomial? How Do You Use a Shortcut to Factor a Perfect Square Trinomial? Virtual Nerd video on factoring trinomials that are perfect squares of binomials Video includes how to recognize the pattern of a perfect square trinomial formula for the factors of a perfect square trinomial (the shortcut) an example, using the formula and a step-by-step procedure Time 8:10 Factoring Polynomials

167 Link: Ex: Factor a Perfect Square TrinomialEx: Factor a Perfect Square TrinomialLink: Ex: Factor a Perfect Square TrinomialEx: Factor a Perfect Square Trinomial Mathispower4u video examples of the special case of factoring quadratic polynomials that are perfect square trinomials Does not rely on memorized formula for factoring; instead uses a modified trial and error method given that the degree 2 and constant terms are perfect squares Time 5:33 Factoring Polynomials

168 Link: Factoring QuadraticsFactoring QuadraticsLink: Factoring QuadraticsFactoring Quadratics Purplemath text lesson on factoring quadratic polynomials Topics and examples include the simple case where the leading coefficient is 1 the hard case where the leading coefficient is not 1, using both the trial and error method and the box method the weird case of quadratic type polynomials that are not actually quadratic Factoring Polynomials

169 Link: Factoring Trinomials with a Leading 1Factoring Trinomials with a Leading 1Link: Factoring Trinomials with a Leading 1Factoring Trinomials with a Leading 1 Khan Academy video example of factoring a quadratic polynomial with leading coefficient 1 Video includes an explanation of what to look for (and why) in the coefficients of the quadratic in order to find the factors Method is illustrated with an example Time 4:12 Factoring Polynomials

170 Link: Factoring a Trinomial with Leading Coefficient of 1 - The Basics Factoring a Trinomial with Leading Coefficient of 1 - The Basics Link: Factoring a Trinomial with Leading Coefficient of 1 - The Basics Factoring a Trinomial with Leading Coefficient of 1 - The Basics Mathispower4u video examples of factoring a quadratic polynomial with leading coefficient 1 Video includes an explanation of what to look for (and why) in the coefficients of the quadratic in order to find the factors Method is illustrated with numerous examples, including one in which the terms of a trinomial have a common factor Time 10:34 Factoring Polynomials

171 Link: Factoring Quadratic ExpressionsFactoring Quadratic ExpressionsLink: Factoring Quadratic ExpressionsFactoring Quadratic Expressions Khan Academy video examples of factoring a quadratic polynomial with leading coefficient 1 Video includes an explanation of what to look for (and why) in the coefficients of the quadratic in order to find the factors Method is illustrated with many examples, including one in which the terms of a trinomial have a common factor Time 16:30 Factoring Polynomials

172 Link: Factoring Trinomials: Trial and Error and GroupingFactoring Trinomials: Trial and Error and GroupingLink: Factoring Trinomials: Trial and Error and GroupingFactoring Trinomials: Trial and Error and Grouping Mathispower4u video examples of factoring a quadratic polynomial where the leading coefficient is not 1 Video includes trial and error (or reverse FOIL) method with an explanation of the procedure and several examples grouping method with several examples Time 9:45 Factoring Polynomials

173 Link: Factoring ax^2+bx+c (Part 1)Factoring ax^2+bx+c (Part 1)Link: Factoring ax^2+bx+c (Part 1)Factoring ax^2+bx+c (Part 1) AlRichards314 video examples of factoring a quadratic polynomial where the leading coefficient is not 1 Method used is a combination of trial and error (or reverse FOIL) and grouping Part 2 includes more examples Part 2 Time 5:22 Factoring Polynomials

174 Link: Factoring ax^2+bx+c (Part 2)Factoring ax^2+bx+c (Part 2)Link: Factoring ax^2+bx+c (Part 2)Factoring ax^2+bx+c (Part 2) AlRichards314 video examples of factoring a quadratic polynomial where the leading coefficient is not 1 Method used is a combination of trial and error (or reverse FOIL) and grouping Continuation of Part 1 with more examplesPart 1 Time 4:49 Factoring Polynomials

175 Link: Factoring Trinomials with a Common FactorFactoring Trinomials with a Common FactorLink: Factoring Trinomials with a Common FactorFactoring Trinomials with a Common Factor Khan Academy video example of factoring a quadratic polynomial in which the terms have a numerical common factor Method used is a combination of trial and error (or reverse FOIL) and grouping Time 5:01 Factoring Polynomials

176 Link: Practice: Factoring Quadratics 1Practice: Factoring Quadratics 1Link: Practice: Factoring Quadratics 1Practice: Factoring Quadratics 1 Khan Academy interactive practice problems on factoring quadratic polynomials with leading coefficient 1 A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Factoring Polynomials

177 Link: Practice: Factoring Quadratics 2Practice: Factoring Quadratics 2Link: Practice: Factoring Quadratics 2Practice: Factoring Quadratics 2 Khan Academy interactive practice problems on factoring quadratic polynomials where the leading coefficient is not 1 A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Factoring Polynomials

178 Link: Factor by GroupingFactor by GroupingLink: Factor by GroupingFactor by Grouping Mathispower4u video examples of factoring polynomials using the grouping method Video includes introduction to the grouping method via an example written description of the steps in the grouping method several examples of factoring cubic polynomials by grouping example using grouping to solve a quadratic equation by factoring Time 7:48 Factoring Polynomials

179 Link: Ex: Factor a Polynomial Using the Grouping TechniqueEx: Factor a Polynomial Using the Grouping TechniqueLink: Ex: Factor a Polynomial Using the Grouping TechniqueEx: Factor a Polynomial Using the Grouping Technique Mathispower4u video examples of factoring cubic polynomials using the grouping method Time 3:51 Factoring Polynomials

180 Link: Factoring by Grouping and Factoring CompletelyFactoring by Grouping and Factoring CompletelyLink: Factoring by Grouping and Factoring CompletelyFactoring by Grouping and Factoring Completely Khan Academy video examples of factoring quadratic polynomials using the grouping method Includes an example of a trinomial in which the terms have a common factor Time 13:57 Factoring Polynomials

181 Link: Example: Basic GroupingExample: Basic GroupingLink: Example: Basic GroupingExample: Basic Grouping Khan Academy video example of factoring an expression with 4 terms in 2 variables using the grouping technique Time 3:46 Factoring Polynomials

182 Link: Factoring PolynomialsFactoring PolynomialsLink: Factoring PolynomialsFactoring Polynomials The Cool Math Guy video examples of factoring polynomials Video includes factoring out the greatest common factor of the terms factoring quadratic polynomials factoring by grouping Time 9:56 Factoring Polynomials

183 Link: Practice: Factoring Polynomials by GroupingPractice: Factoring Polynomials by GroupingLink: Practice: Factoring Polynomials by GroupingPractice: Factoring Polynomials by Grouping Khan Academy interactive practice problems on factoring polynomials using the grouping technique A sequence of five practice problems is provided, along with help with correct formats to enter answers hints to help solve the problem, if needed links to video lessons if you get stuck Factoring Polynomials

184 Formulas & Polynomials in Two (or more) Variables Description and examples of formulas and polynomial equations, including evaluation at specific numbers and solving for one variable in terms of the others Equations and Formulas Writing a Polynomial Expression from a Verbal Phrase Evaluating Formulas and Polynomials for Specific Values of the Variables Evaluating Formulas and Polynomials for Specific Values of the Variables Solving for One Variable in Terms of the Others in a Formula Interactive Practice Problems: Solving Equations in Terms of a Variable Interactive Practice Problems: Solving Equations in Terms of a Variable Return to Topics List CONTENTS:

185 Link: Equations and FormulasEquations and FormulasLink: Equations and FormulasEquations and Formulas Math Is Fun text lesson on equations, formulas, and the difference between them Formulas & Polynomials in Two (or more) Variables

186 Link: Example Question Involving PolynomialsExample Question Involving PolynomialsLink: Example Question Involving PolynomialsExample Question Involving Polynomials Tutortag video example of translating a verbal phrase into a polynomial expression Example expresses the difference in areas between two geometric figures whose dimensions are given as variables Time 5:34 Formulas & Polynomials in Two (or more) Variables

187 Link: Evaluate a Formula Using SubstitutionEvaluate a Formula Using SubstitutionLink: Evaluate a Formula Using SubstitutionEvaluate a Formula Using Substitution Khan Academy video example using substitution in a formula to convert degrees Celsius to degrees Fahrenheit Time 1:15 Formulas & Polynomials in Two (or more) Variables

188 Link: Evaluating a Polynomial at a Given ValueEvaluating a Polynomial at a Given ValueLink: Evaluating a Polynomial at a Given ValueEvaluating a Polynomial at a Given Value Khan Academy video example of substitution of a negative number in a quadratic polynomial expression Time 1:09 Formulas & Polynomials in Two (or more) Variables

189 Link: How Do You Evaluate an Algebraic Expression by Plugging in Values? How Do You Evaluate an Algebraic Expression by Plugging in Values? Link: How Do You Evaluate an Algebraic Expression by Plugging in Values? How Do You Evaluate an Algebraic Expression by Plugging in Values? Virtual Nerd video example of evaluating a polynomial expression in two variables at given values of the variables Time 1:07 Formulas & Polynomials in Two (or more) Variables

190 Link: Polynomial Expressions and Polynomial FunctionsPolynomial Expressions and Polynomial FunctionsLink: Polynomial Expressions and Polynomial FunctionsPolynomial Expressions and Polynomial Functions Mathispower4u video examples of substitution of numbers in polynomial expressions Video includes review of polynomial terminology examples of evaluation of polynomials in more than one variable at specific values of the variables evaluation of polynomial expressions in one variable at specific numbers both by hand and using a graphing calculator Time 7:25 Formulas & Polynomials in Two (or more) Variables

191 Link: Evaluate a Quadratic Equation - Death ApplicationEvaluate a Quadratic Equation - Death ApplicationLink: Evaluate a Quadratic Equation - Death ApplicationEvaluate a Quadratic Equation - Death Application Mathispower4u video example evaluating a quadratic polynomial at a number Polynomial formula models a real-world problem and includes non-integer (decimal) coefficients A calculator is used for most of the calculations Time 4:52 Formulas & Polynomials in Two (or more) Variables

192 Link: Evaluate a Polynomial Equation - Flu Virus ApplicationEvaluate a Polynomial Equation - Flu Virus ApplicationLink: Evaluate a Polynomial Equation - Flu Virus ApplicationEvaluate a Polynomial Equation - Flu Virus Application Mathispower4u video example evaluating a fourth degree polynomial at a number Polynomial formula models a real-world problem and includes non-integer (decimal) coefficients A calculator is used for some of the calculations Time 4:01 Formulas & Polynomials in Two (or more) Variables

193 Link: Solving Equations and FormulasSolving Equations and FormulasLink: Solving Equations and FormulasSolving Equations and Formulas Slide Share text slides with examples of formulas in more than one variable and solving for one variable in terms of the others Emphasizes undoing operations to isolate the desired variable Formulas & Polynomials in Two (or more) Variables

194 Link: Solving Literal EquationsSolving Literal EquationsLink: Solving Literal EquationsSolving Literal Equations Purplemath text lesson on solving for one variable in terms of the others in a formula with two or more variables Topics and examples include geometric and other types of formulas in three or more variables rewriting a linear equation in slope-intercept form to find the slope of the line Formulas & Polynomials in Two (or more) Variables

195 Link: Rearrange Formulas to Isolate Specific VariablesRearrange Formulas to Isolate Specific VariablesLink: Rearrange Formulas to Isolate Specific VariablesRearrange Formulas to Isolate Specific Variables Khan Academy video example solving the area of a triangle formula for the height in terms of the area and base Time 2:29 Formulas & Polynomials in Two (or more) Variables

196 Link: Solving for a VariableSolving for a VariableLink: Solving for a VariableSolving for a Variable Khan Academy video example solving the rectangle perimeter formula for the length in terms of the perimeter and width Time 1:24 Formulas & Polynomials in Two (or more) Variables

197 Link: Example: Solving for a VariableExample: Solving for a VariableLink: Example: Solving for a VariableExample: Solving for a Variable Khan Academy video example solving the rectangle perimeter formula for the width in terms of the perimeter and length Problem is solved in various ways Time 6:58 Formulas & Polynomials in Two (or more) Variables

198 Link: Solving for a Variable 2Solving for a Variable 2Link: Solving for a Variable 2Solving for a Variable 2 Khan Academy video example solving for the Fahrenheit temperature in the formula giving the Celsius temperature in terms of the Fahrenheit temperature Time 2:41 Formulas & Polynomials in Two (or more) Variables

199 Link: Solving Equations in Terms of a VariableSolving Equations in Terms of a VariableLink: Solving Equations in Terms of a VariableSolving Equations in Terms of a Variable Khan Academy interactive practice problems on solving for one variable in terms of the others in an equation in two or more variables A sequence of five practice problems is provided, along with hints to help solve the problem, if needed links to video lessons if you get stuck Formulas & Polynomials in Two (or more) Variables

200 Polynomial Functions Description and examples of the behavior of polynomial functions, including end behavior, smoothness, turning points, and graphs End Behavior of Polynomial Function General Properties of Polynomial Functions Return to Topics List CONTENTS:

201 Link: Summary of End Behavior of Polynomial FunctionSummary of End Behavior of Polynomial FunctionLink: Summary of End Behavior of Polynomial FunctionSummary of End Behavior of Polynomial Function Mathispower4u video describing the end (or long run) behavior of a polynomial in terms of the degree and the sign of the leading coefficient Time 5:48 Polynomial Functions

202 Link: How Polynomials BehaveHow Polynomials BehaveLink: How Polynomials BehaveHow Polynomials Behave Math Is Fun text lesson on the behavior of the graphs of polynomial functions Topics and examples include continuity and smoothness behavior of x n for even and odd values of n behavior of ax n for various values of a turning points end behavior Polynomial Functions

203 Link: Polynomial Graphs: General BehaviorPolynomial Graphs: General BehaviorLink: Polynomial Graphs: General BehaviorPolynomial Graphs: General Behavior Purplemath text lesson on the behavior of the graphs of polynomial functions Topics and examples include end behavior zeroes and their multiplicities degrees and turning points quick graphing Polynomial Functions

204 Link: Characteristics of Polynomial FunctionsCharacteristics of Polynomial FunctionsLink: Characteristics of Polynomial FunctionsCharacteristics of Polynomial Functions AlRichards314 video introduction to the behavior of graphs of polynomial functions Topics and examples include general shape of graphs of linear, quadratic, cubic, and quartic polynomials using finite differences to determine the degree of a polynomial given by a table of values Time 9:53 Polynomial Functions

205 Link: How to Graph PolynomialsHow to Graph PolynomialsLink: How to Graph PolynomialsHow to Graph Polynomials For Dummies text lesson on graphing polynomial functions Topics and examples include plotting the intercepts end behavior determining whether the graph is below or above the axis between each pair of intercepts sketching the graph Polynomial Functions


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