Week 3 Day 1

Bring every assignment to next class for a progress report.

Chapter 1 Fundamental Concepts 1.6 Algebraic Expressions Add and Subtract 1.7 Exponents and Radicals 1.8 Multiplication of Algebraic Expressions 1.9 Division of Algebraic Expressions 1.10 Linear Equations 1.13 Applications Involving Linear Equations 1.14 Ratio and Proportions 1.11 and 1.12 previously covered.

1.6 ALGEBRAIC EXPRESSIONS page21 Definitions help when later you read how to work a problem, you have to know what the words mean in the context of mathematics. Exercises 1.6 Classify each expression as a monomial, a binomial, or a trinomial. Find the degree of each monomial. Find the degree of each polynomial.

Look at the questions you have to answer and then read the section. Exercises 1.7 Page 30

Exercises 1.7 Page 31 Problems and calculator operations.

Exercises 1.8 Assigned 2, 4, 6 So don’t go deep into section.

Exercises 1.9 page 37 Home work.

Exercises 1.10 Assigned 4, 6, 8

1.6 ALGEBRAIC EXPRESSIONS page 21 In an expression a variable quantity may be represented by a letter. A does not equal a. A constant may also be represented by a letter. The letter may be replaced by only one number.

1.6 ALGEBRAIC EXPRESSIONS page 21 A term is an expression or part of an expression involving only the product of numbers or letters. Terms may have two or more factors connected by signs indicating multiplication. The term 7xyz has four factors: 7, x, y, and z.

1.6 ALGEBRAIC EXPRESSIONS page 21 The coefficient of a factor (or factors) is the product of the remaining factors. For 7xyz: the coefficient of xyz is 7 the coefficient of 7z is xy

page 22 An algebraic expression containing only one term is called a monomial. A binomial is an expression containing two terms. A trinomial expression contains three terms.

1.6 ALGEBRAIC EXPRESSIONS page 22 A term is an expression or part of an expression involving only the product of numbers or letters.

page 22 A polynomial is in decreasing order if each term is of some degree less than the preceding term.

ALGEBRAIC EXPRESSIONS page 23 To add and subtract algebraic expressions, combine like terms. Like terms have identical letters and powers of letters.

ADDING ALGEBRAIC EXPRESSIONS page 23 Combining like terms; First method.

ADDING ALGEBRAIC EXPRESSIONS page 23 Combining like terms; First method.

ADDING ALGEBRAIC EXPRESSIONS page 23 Combining like terms; First method.

ADDING ALGEBRAIC EXPRESSIONS page 23 Combining like terms for adding; First method.

ADDING ALGEBRAIC EXPRESSIONS page 23 Combining like terms for adding; Second method. Arrange expressions so that the like terms appear in the same column. Reordered with proper sign.

1.6 +

+

SUBTRACTING ALGEBRAIC EXPRESSIONS page 23 To subtract use the subtraction principle: To subtract, add the opposite of each quantity being subtracted.

SUBTRACTING ALGEBRAIC EXPRESSIONS page 23 To subtract, add the opposite of each quantity being subtracted. Negative Being Subtracted Positive Negative

SUBTRACTING ALGEBRAIC EXPRESSIONS page 23 To subtract, add the opposite of each quantity being subtracted.

ADDING and SUBTRACTING

1.7 EXPONENTS AND RADICALS page indicates that the letter a is to be used as a factor four times. We say that is the fourth power of a. it may also be written The factor that is expressed as a power is called the base. The number that indicates the number of times the base is to be used as a factor is the exponent.

degree

Remember section 1.3

1.7 EXPONENTS AND RADICALS page 26-27

How would you answer this without a calculator that does exponents?

Multiply don’t add.

Now for something new.

(3 x y x y x y) x (3 x y x y x y) x (3 x y x y x y) x (3 x y x y x y) (3 x 3 x 3 x 3 x) x y x y x y x y x y x y x y x y x y x y x y x y

Page 28 To show that this law for zero exponents is valid, we use this reasoning.

Page 28 The inverse process of raising a number to a power is called finding the root of a number. The nth root of a number a is written where n is the index, a is the radicand, and the symbol is called a radical sign.

Page 28 The nth root of a number a is written where n is the index.

Concept Page 28

The square root of a product of positive numbers equals the product of the square roots of its factors.

Page 29 A perfect square is the square of a rational number. The first ten positive integral perfect squares are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. This will be very helpful later.

Page 29

1.8 MULTIPLICATION OF ALGEBRAIC EXPRESSIONS page 31 To multiply monomials, multiply their numerical coefficients and multiply each set of like letter factors using the laws of exponents.

A term is an expression or part of an expression involving only the product of numbers or letters.

1.8 MULTIPLICATION OF ALGEBRAIC EXPRESSIONS page 31 The same only slightly more complex:

1.8 MULTIPLICATION OF ALGEBRAIC EXPRESSIONS page 31

EXAMPLE 3 To multiply a multinomial by a monomial, multiply each term of the multinomial by the monomial using the distributive property:

1.8 MULTIPLICATION OF ALGEBRAIC EXPRESSIONS page 31 EXAMPLE 3 distributive property:

1.8 MULTIPLICATION OF ALGEBRAIC EXPRESSIONS page 31 EXAMPLE 3 We can multiply the like terms by each other, leaving the addition.

1.8 MULTIPLICATION OF ALGEBRAIC EXPRESSIONS page 31 Do not do any multiply beyond the + sign.

1.8 MULTIPLICATION OF ALGEBRAIC EXPRESSIONS page 32 EXAMPLE 6

1.8 MULTIPLICATION OF ALGEBRAIC EXPRESSIONS page 32 EXAMPLE 6

1.8 MULTIPLICATION OF ALGEBRAIC EXPRESSIONS page 32 EXAMPLE 6

1.9 DIVISION OF ALGEBRAIC EXPRESSIONS page 35

Do not convert - 9/4 into: 2 ¼ or 2.25

Page 2 A prime number is defined as a positive integer greater than one that is evenly divisible only by itself and one. 1, 2, 3, 5, 7, 11, 13, 17, 19 We will use primes for factoring.

-25 2 x No 3 x No 5 x 5 Factor numbers in to prime numbers.

20 2 x 10 2 x 2 x 5 Factor numbers in to prime numbers x No 3 x No 5 x 5

Factor numbers in to prime numbers.

Long division not assigned Prone to errors.