Intermediate Algebra (11th edition)

(Marvins-Underground-K-12) #1
Dividing Polynomial Functions

For and find and What value


of xis not in the domain of the quotient function?


This quotient was found in Example 2,with mreplacing x. The result here is so


The number 2 is not in the domain because it causes the denominator


to equal 0. Then


Let

Verify that the same value is found by evaluating NOW TRY


ƒ 1 - 32

g 1 - 32.


a x=-3.


ƒ


g


b1- 32 = 21 - 32 + 5 =-1.


g 1 x 2 =x- 2


a xZ 2.


ƒ


g


b1x 2 = 2 x+5,


2 x+5,


a


ƒ


g


b1x 2 =


ƒ 1 x 2


g 1 x 2


=


2 x^2 +x- 10


x- 2


A


ƒ

A gB^1 -^32.


ƒ

ƒ 1 x 2 = 2 x g 1 x 2 =x-2, gB 1 x 2


(^2) +x- 10


EXAMPLE 6


306 CHAPTER 5 Exponents, Polynomials, and Polynomial Functions


NOW TRY
EXERCISE 6
For
and


find and A
ƒ
A gB 182.
ƒ
gB^1 x^2


g 1 x 2 = 2 x-1,

ƒ 1 x 2 = 8 x^2 + 2 x- 3

NOW TRY ANSWER



  1. 4 x+3, xZ^12 ; 35


Complete solution available
on the Video Resources on DVD


5.5 EXERCISES


Concept Check Complete each statement with the correct word(s).
1.We find the quotient of two monomials by using the rule for.
2.When dividing polynomials that are not monomials, first write them in powers.
3.If a polynomial in a division problem has a missing term, insert a term with coefficient
equal to as a placeholder.
4.To check a division problem, multiply the by the quotient. Then add the.

Divide. See Example 1.













8. 9. 10.


11. 12.


13. 14.


Complete the division.

12 ab^2 c+ 10 a^2 bc+ 18 abc^2
6 a^2 bc

8 wxy^2 + 3 wx^2 y+ 12 w^2 xy
4 wx^2 y

24 h^2 k+ 56 hk^2 - 28 hk
16 h^2 k^2

4 m^2 n^2 - 21 mn^3 + 18 mn^2
14 m^2 n^3

64 x^3 - 72 x^2 + 12 x
8 x^3

15 m^3 + 25 m^2 + 30 m
5 m^3

80 r^2 - 40 r+ 10
10 r

9 y^2 + 12 y- 15
3 y

27 m^4 - 18 m^3 + 9 m
9

15 x^3 - 10 x^2 + 5
5

15. 16.


8 b^2

6 b^3 - 15 b^2

2 b- 5  6 b^3 - 7 b^2 - 4 b- 40

3 b^2


  • 21 r^2


3 r^3 - r^2

3 r- 1  3 r^3 - 22 r^2 + 25 r- 6

r^2
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