Unit 1 Notes. Polynomials

Transcription

1 Unit 1 Notes 1 Day Number Date Topic Problem Set 1 Wed. Sept. Operations with Signed Numbers and Order of Operations Pre-Unit Review PS (1 ) Thurs. Sept. Working with Exponents Start Exponent Laws P.S. #1.1 ( ) Fri. Sept. 8 Finish Exponent Laws P.S. #1. ( ) Mon. Sept. 11 Collecting Like Terms/Adding P.S. #1. ( 8) Tues. Sept. 1 Distributive Property Subtracting P.S. #1. (9 10) Wed. Sept. 1 Quiz #1 Practice P.S. #1. (11 1) 8 9 Thurs. Sept. 1 Fri. Sept. 1 Review and Catch up Pages 1-1:, 8 0 Review Review Sheet for Test #1 10 Mon. Sept. 18 Test #1 TBD Name:

2 Adding and Subtracting Integers Rules: When combining integers with the, just the numbers and the sign. When combining integers with, just the numbers and the sign. Examples: + = (-) + = + (-) = (-) + (-) = = (-) = (-) = (-) (-) = Provide real life situations for the following: a.) b.) c.) 1 1 Multiplying and Dividing Integers The rule that you are about to learn works for multiplying and dividing, only. It does not work for adding and subtracting integers!! Love Hate = = = = = = = = Examples: x = (-) x = x (-) = (-) x (-) = 1 = -1 = 9 (-) = (-) (-8) =

3 BEDMAS Review BEDMAS is a pneumonic device used to help you remember the. When doing any sort of algebra or arithmetic, you MUST follow BEDMAS. B E D A M S Examples: 1.) 1 (-).) 1 ( )().) Evaluate (10 + x), for x = -.) Evaluate 1 + (x + 1), for x =

4 Examples involving exponential notation. Also, identify the base and exponent in each expression. 1.) Base: Exponent: Did you notice that parentheses are used in,, and? Why do you think there are parentheses?.) Base: Exponent:.) 11 Base: Exponent:.) Base: Exponent: Vocabulary The number x n is called raised to the power, is the exponent and is the base..).8 Base: Exponent: Will these products be positive or negative? How do you know? Is it necessary to do all of the calculations to determine the sign of the product? Why or why not? Fill in the blanks about whether the number is positive or negative. If n is a positive even number, then If n is a positive odd number, then n ( ) is. n ( ) is. Expand and evaluate 1. Expand and evaluate: Try these exercises on your own. Then, compare with your partner(s).

5 Exponent Laws 1.) Expand.) Expand What do you notice? a a. What do you notice? When you find the product of two algebraic expressions with the same base, you can their exponents and use this exponent with the base. Simplify each expression. Write your answer in exponential notation. a 9.) ( ) ( ).).) a.) Expand.) Expand. What do you notice? y y. What do you notice? When you find the quotient of two algebraic expressions with the same base, you can their exponents and use this exponent with the base. Simplify each expression. Write your answer in exponential notation. 9 8.) 9.) ( ) ( ) 10.) x y x y

6 Simplify each expression. Write your answer in exponential notation. 1.).) ) x y y x x y.).) b a 9a a b a.) What does ( ) mean? What does (n ) mean? What do you notice? When you raise a power to a power, the base and the exponents. Simplify each expression. Write your answer in exponential notation..) ( 1 ) 9 8.) (( ) ) 8 9.) 1 ) (a 10.) a b c 11.) x 1.) a 1.) Use the of a quotient property to simplify each expression. Write the quotient as an exponent. Expression Exponent 1.) What expression did you write for? What was the exponent? 1.) Using factored form, find the value of.

7 1.) Based on your findings, what can you conclude about the value of 0? 1.) Make a prediction about the value of any number raised to the zero power. 18.) Use a calculator to check your prediction for several numbers. Is your prediction right? A nonzero number raised to the zero power is equal to. Simplify each expression and evaluate where applicable. 19.) 0 0.) ) 8.) 0 ( a a ) a Definitions: Monomial Binomial Trinomial Polynomial Degree Like Terms For 1, identify the coefficient, the variable, and the degree. 1. x. h coefficient = coefficient = variable = variable = degree = degree =. a b coefficient = variable = degree =

8 8 For, put the polynomial in descending order and identify the degree of the polynomial.. x x. x x x 8x. 1ab 9a b 8a For 9, collect like terms:. 8n n 8. x 8 + 1x b 11b +.8 Finding sums of polynomials: x x x 8x 1.) Underline each in a different way..) Every time you have a new like term,..) Make sure your answer is written in. 1.) (8y y ) (y y ).) (x x x ) (x 9x x ).) (r r ) (r r ).) (1y 9y 8y ) (y 1 y y ) Perimeter: The around a. Find the perimeter of each..).) 9c x c 8c c 1c

9 Reminder: Notes 1. Distributive Property When you multiply monomials, you must always exponents. Distribute: When you distribute, you must multiply the number on the of the parentheses by number on the of the parentheses. 9 Try These: 1. (x + 8). c(c + ). d(d + ). a(a + ab). 1x (x ). 9j ( j j ) ( x y ) (x y ) x 9. If the length of a rectangle is L and the width of a rectangle is L +. What is the area of the rectangle? 10. y 1 y 11. r r 1

10 10 Notes 1. Subtracting Finding differences of polynomials: x x x 8x 1.) Make the subtraction sign in between each expression positive and all the signs in the expression..) Underline each in a different way..) Every time you have a new like term,..) Make sure your answer is written in. 1.) (8y y ) (y y ).) (x x x ) (x 9x x ).) r r r r.) 1y 9y 8y y 1 y y. Perimeter = 1x + x + 8. Perimeter = b x? x 9 x b 8? 1x 1b