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144 a 6 + 90 a 3

18 a 3 (8 a 3 + 5)

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10 y 2 + 50 y + 40

10( y 2 + 5 y + 4)

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12 u 2 36 u 108

12( u 2 − 3 u − 9)

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3 a 4 24 a 3 + 18 a 2

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5 p 4 20 p 3 15 p 2

5 p 2 ( p 2 − 4 p − 3)

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11 x 6 + 44 x 5 121 x 4

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8 c 5 + 40 c 4 56 c 3

8 c 3 ( c 2 + 5 c − 7)

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−7 p 84

−7( p + 12)

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−18 b 2 66 b

−6 b (3 b + 11)

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−8 a 3 + 32 a 2

−8 a 2 ( a − 4)

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−9 b 5 + 63 b 3

−9 b 3 ( b 2 − 7)

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Everyday math

Revenue A manufacturer of microwave ovens has found that the revenue received from selling microwaves a cost of p dollars each is given by the polynomial −5 p 2 + 150 p . Factor the greatest common factor from this polynomial.

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Height of a baseball The height of a baseball hit with velocity 80 feet/second at 4 feet above ground level is −16 t 2 + 80 t + 4 , with t = the number of seconds since it was hit. Factor the greatest common factor from this polynomial.

−4(4 t 2 − 20 t − 1)

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Writing exercises

The greatest common factor of 36 and 60 is 12 . Explain what this means.

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What is the GCF of y 4 , y 5 , and y 10 ? Write a general rule that tells how to find the GCF of y a , y b , and y c .

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

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Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?

Chapter review exercises

Add and Subtract Polynomials

Identify Polynomials, Monomials, Binomials and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

y 2 + 8 y 20

trinomial

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n 3 3 n 2 + 3 n 1

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Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

16 x 2 40 x 25

2

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Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

Add 4 n 5 , n 5 , −6 n 5

−3 n 5

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Subtract 10 x 2 from 3 x 2

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Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

( 4 a 2 + 9 a 11 ) + ( 6 a 2 5 a + 10 )

10 a 2 + 4 a − 1

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( 8 m 2 + 12 m 5 ) ( 2 m 2 7 m 1 )

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( y 2 3 y + 12 ) + ( 5 y 2 9 )

6 y 2 − 3 y + 3

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( 5 u 2 + 8 u ) ( 4 u 7 )

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Find the sum of 8 q 3 27 and q 2 + 6 q 2

8 q 3 + q 2 + 6 q − 29

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Find the difference of x 2 + 6 x + 8 and x 2 8 x + 15

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Evaluate a Polynomial for a Given Value of the Variable

In the following exercises, evaluate each polynomial for the given value.

200 x 1 5 x 2 when x = 5

995

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200 x 1 5 x 2 when x = 0

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200 x 1 5 x 2 when x = 15

2,955

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5 + 40 x 1 2 x 2 when x = 10

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5 + 40 x 1 2 x 2 when x = −4

−163

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5 + 40 x 1 2 x 2 when x = 0

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A pair of glasses is dropped off a bridge 640 feet above a river. The polynomial −16 t 2 + 640 gives the height of the glasses t seconds after they were dropped. Find the height of the glasses when t = 6 .

64 feet

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The fuel efficiency (in miles per gallon) of a bus going at a speed of x miles per hour is given by the polynomial 1 160 x 2 + 1 2 x . Find the fuel efficiency when x = 20 mph.

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Use Multiplication Properties of Exponents

Simplify Expressions with Exponents

In the following exercises, simplify.

Simplify Expressions Using the Product Property of Exponents

In the following exercises, simplify each expression.

Simplify Expressions Using the Power Property of Exponents

In the following exercises, simplify each expression.

Practice Key Terms 1

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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