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Section 5.1 Polynomials Addition And Subtraction

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OBJECTIVES A Classify polynomials.

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**OBJECTIVES Find the degree of a polynomial and write descending order.**

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OBJECTIVES C Evaluate a polynomial.

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OBJECTIVES D Add or subtract polynomials.

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OBJECTIVES E Solve applications involving sums or differences of polynomials.

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**Degree of a Polynomial in One Variable**

DEFINITION Degree of a Polynomial in One Variable The degree of a polynomial in one variable is the greatest exponent of that variable.

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**Degree of a Polynomial in Several Variables**

DEFINITION Degree of a Polynomial in Several Variables The greatest sum of the exponents of the variables in any one term of the polynomial.

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**Properties for Adding Polynomials**

RULES Properties for Adding Polynomials

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**Properties for Adding Polynomials**

RULES Properties for Adding Polynomials

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**Properties for Adding Polynomials**

RULES Properties for Adding Polynomials

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**Subtracting Polynomials**

RULES Subtracting Polynomials

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Chapter 5 Section 5.1A,B Exercise #1

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**Classify as a monomial, binomial, or trinomial and**

give the degree. Binomial. Degree is determined by comparing Degree 8

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Chapter 5 Section 5.1D Exercise #5

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METHOD 1

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METHOD 2

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Chapter 5 Section 5.1D Exercise #6

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METHOD 1

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METHOD 1

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METHOD 1

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METHOD 2

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Section 5.2 Multiplication of Polynomials

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OBJECTIVES A Multiply a monomial by a polynomial.

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OBJECTIVES B Multiply two polynomials.

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OBJECTIVES C Use the FOIL method to multiply two binomials.

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OBJECTIVES D Square a binomial sum or difference.

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OBJECTIVES E Find the product of the sum and the difference of two terms.

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OBJECTIVES F Use the ideas discussed to solve applications.

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**Multiplication of Polynomials**

RULES Multiplication of Polynomials

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USING FOIL To Multiply Two Binomials (x + a)(x + b)

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RULE To Square a Binomial Sum

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RULE To Square a Binomial Difference

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**Sum and Difference of Same Two Monomials**

PROCEDURE Sum and Difference of Same Two Monomials

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Chapter 5 Section 5.2B,C Exercise #8a

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METHOD 1

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METHOD 2

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Chapter 5 Section 5.2D Exercise #9b

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Chapter 5 Section 5.2E Exercise #10

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**Product of Sum and Difference of Same Two Monomials**

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Section 5.3 The Greatest Common Factor and Factoring by Grouping

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OBJECTIVES A Factor out the greatest common factor in a polynomial.

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OBJECTIVES B Factor a polynomial with four terms by grouping.

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**GREATEST COMMON FACTOR**

is the Greatest Common monomial Factor (GCF) of a polynomial in x if: 1. a is the greatest integer that divides each coefficient.

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**GREATEST COMMON FACTOR**

is the Greatest Common monomial Factor (GCF) of a polynomial in x if: 2. n is the smallest exponent of x in all the terms.

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**PROCEDURE Factoring by Grouping Group terms with common**

factors using the associative property.

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PROCEDURE Factoring by Grouping Factor each resulting binomial.

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**PROCEDURE Factoring by Grouping Factor out the binomial**

using the GCF, by the distributive property.

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Chapter 5 Section 5.3B Exercise #12

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Section 5.4 Factoring Trinomials

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OBJECTIVES A Factor a trinomial of the form

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OBJECTIVES B Factor a trinomial of the form using trial and error.

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OBJECTIVES C Factor a trinomial of the form using the ac test.

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PROCEDURE Factoring Trinomials

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**RULE The ac Test is factorable only if there are two integers**

whose product is ac and sum is b.

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Chapter 5 Section 5.4A,B,C Exercise #13b

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**The ac Method Find factors of ac (–20) whose sum is (1) and replace the middle term (xy).**

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Section 5.5 Special Factoring

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OBJECTIVES A Factor a perfect square trinomial.

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OBJECTIVES B Factor the difference of two squares.

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OBJECTIVES C Factor the sum or difference of two cubes.

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**Factoring Perfect Square Trinomials**

PROCEDURE Factoring Perfect Square Trinomials

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**Factoring the Difference of**

PROCEDURE Factoring the Difference of Two Squares

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**Factoring the Sum and Difference of Two Cubes**

PROCEDURE Factoring the Sum and Difference of Two Cubes

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Chapter 5 Section 5.5A Exercise #15a

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Chapter 5 Section 5.5 Exercise #16

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**Difference of Two Squares**

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Chapter 5 Section 5.5B Exercise #17

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**Perfect Square Trinomial**

Difference of Two Squares

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Chapter 5 Section 5.5c Exercise #18a

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Sum of Two Cubes

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Section 5.6 General Methods of Factoring

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**OBJECTIVES Factor a polynomial using the procedure given in the text.**

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**PROCEDURE A General Factoring Strategy Factor out the GCF, if**

there is one. Look at the number of terms in the given polynomial.

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**PROCEDURE A General Factoring Strategy**

If there are two terms, look for:

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**PROCEDURE A General Factoring Strategy**

If there are two terms, look for:

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**PROCEDURE A General Factoring Strategy**

If there are two terms, look for:

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**PROCEDURE A General Factoring Strategy**

If there are two terms, look for: The sum of two squares, is not factorable.

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**PROCEDURE A General Factoring Strategy**

If there are three terms, look for: Perfect square trinomial

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**PROCEDURE A General Factoring Strategy**

If there are three terms, look for: Trinomials of the form

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**PROCEDURE A General Factoring Strategy Use the ac method or**

trial and error.

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**PROCEDURE A General Factoring Strategy If there are four terms:**

Factor by grouping.

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**PROCEDURE A General Factoring Strategy Check the result by**

multiplying the factors.

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Chapter 5 Section 5.6A Exercise #20b

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**Perfect Square Trinomial**

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Chapter 5 Section 5.6A Exercise #21

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**The ac Method Find factors of ac (–12) whose sum is (–11) and replace the middle term (–11xy).**

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**The ac Method Find factors of ac (–12) whose sum is (–11) and replace the middle term (–11xy).**

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Chapter 5 Section 5.6A Exercise #22

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**Difference of Two Squares**

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Section 5.7 Solving Equations by Factoring: Applications

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OBJECTIVES A Solve equations by factoring.

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OBJECTIVES B Use Pythagorean theorem to find the length of one side of a right triangle when the lengths of the other two sides are given.

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OBJECTIVES C Solve applications involving quadratic equations.

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**PROCEDURE Set equation equal to 0. O Factor Completely. F**

Set each linear Factor equal to 0 and solve each. F

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DEFINITION Pythagorean Theorem c a b

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Chapter 5 Section 5.7A Exercise #23b

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O F F or or

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