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
- 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