holt mcdougal algebra 1 6-5 multiplying polynomials 6-1 integer exponents holt algebra 1 warm up...

Holt McDougal Algebra 1

6-5 Multiplying Polynomials6-1 Integer Exponents

Holt Algebra 1

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Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz



6-5 Multiplying Polynomials

Warm UpEvaluate each expression for the given values of the variables.

1. x3y2 for x = –1 and y = 10

2. for x = 4 and y = (–7)

Write each number as a power of the given base.

–100

433. 64; base 4

(–3)34. –27; base (–3)



Evaluate expressions containing zero and integer exponents.

Simplify expressions containing zero and integer exponents.

Objectives



You have seen positive exponents. Recall that to simplify 32, use 3 as a factor 2 times: 32 = 3 3 = 9.

But what does it mean for an exponent to be negative or 0? You can use a table and look for a pattern to figure it out.

3125 625 125 25 5

5

Power

Value

55 54 53 52 51 5–150 5–2

5 5 5



When the exponent decreases by one, the value of the power is divided by 5. Continue the pattern of dividing by 5.



Base

x

Exponent

Remember!

4



Notice the phrase “nonzero number” in the

previous table. This is because 00 and 0 raised to

a negative power are both undefined. For

example, if you use the pattern given above the

table with a base of 0 instead of 5, you would get

0º = . Also 0–6 would be = . Since division by

0 is undefined, neither value exists.



2–4 is read “2 to the negative fourth power.”

Reading Math



Example 1: Application

One cup is 2–4 gallons. Simplify this expression.

gal is equal to



Check It Out! Example 1

A sand fly may have a wingspan up to 5–3 m. Simplify this expression.

5-3 m is equal to



Example 2: Zero and Negative Exponents

Simplify.

A. 4–3

B. 70

7º = 1Any nonzero number raised to the zero

power is 1.

C. (–5)–4

D. –5–4



In (–3)–4, the base is negative because the

negative sign is inside the parentheses. In –3–4

the base (3) is positive.

Caution


6-5 Multiplying Polynomials6-5 Multiplying Polynomials

Holt Algebra 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz




Warm UpEvaluate.

1. 32

3. 102

Simplify.

4. 23 24

6. (53)2

9 16

100

27

2. 24

5. y5 y4

56 7. (x2)4

8. –4(x – 7) –4x + 28

y9

x8



Multiply polynomials.

Objective



To multiply monomials and polynomials, you will use some of the properties of exponents that you learned earlier in this chapter.



Multiply.

Example 1: Multiplying Monomials

A. (6y3)(3y5)

(6y3)(3y5)

18y8

Group factors with like bases together.

B. (3mn2) (9m2n)

(3mn2)(9m2n)

27m3n3

Multiply.


Multiply.

(6 3)(y3 y5)

(3 9)(m m2)(n2 n)



Multiply.

Example 1C: Multiplying Monomials

4 53s t


Multiply.

22 2112

4ts tt s s

••

•

2 21−12

4t s ts ts

2• •

14 s2 t2 (st) (-12 s t2)



When multiplying powers with the same base, keep the base and add the exponents.

x2 x3 = x2+3 = x5

Remember!



Check It Out! Example 1

Multiply.

a. (3x3)(6x2)

(3x3)(6x2)

(3 6)(x3 x2)

18x5


Multiply.


Multiply.

b. (2r2t)(5t3)

(2r2t)(5t3)

(2 5)(r2)(t3 t)

10r2t4



Check It Out! Example 1 Continued

Multiply.


Multiply.

c.

4 52 2112

3x zy zx y

3

2112

3x y x z y z

2 4 53

3 22 4 5112 z

3zx x y y

7554x y z

• • • •

holt mcdougal algebra 1 6-5 multiplying polynomials 6-1 integer exponents holt algebra 1 warm up...

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