For each pair of functions, find the quotient and give any x-values that are not in the
domain of the quotient function. See Example 6.
61.ƒ 1 x 2 = 10 x 2 - 2 x, g 1 x 2 = 2 x 62.ƒ 1 x 2 = 18 x 2 - 24 x, g 1 x 2 = 3 xA
ƒ
gB^1 x^2308 CHAPTER 5 Exponents, Polynomials, and Polynomial Functions
63. , 64. ,
65.ƒ 1 x 2 = 8 x 3 - 27 , g 1 x 2 = 2 x - 3 66.ƒ 1 x 2 = 27 x^3 + 64 , g 1 x 2 = 3 x+ 4ƒ 1 x 2 = 2 x^2 - x- 3 g 1 x 2 =x+ 1 ƒ 1 x 2 = 4 x^2 - 23 x- 35 g 1 x 2 =x- 7Let , , and. Find each of the following. See Example 6.71. 72. 73. 74.
75. 76. 77. 78.
Use the distributive property to rewrite each expression. See Section 1.4.
- 9 # 6 + 9 #r^2 83. 712 x 2 - 713 z 2 84. 3 x 1 x+ 12 + 41 x+ 12
81 y- 52 - 12 x- 112 4 p 12 p+ 12PREVIEW EXERCISES
ah
gba-3
2
a bh
gba-1
2
a bƒ
gba3
2
a bƒ
gba1
2
bag
ha b1- 12h
g
a b1 32g
ha b1x 2h
g
b1x 2aƒ
ha b1 12ƒ
ga b1 22ƒ
ha b1x 2ƒ
gb1x 2ƒ 1 x 2 =x^2 - 9 g 1 x 2 = 2 x h 1 x 2 =x- 35.1
exponent
base
exponential (power)
5.2
term
algebraic expression
polynomial
numerical coefficient
(coefficient)
degree of a term
polynomial in x
descending powers
leading term
leading coefficienttrinomial
binomial
monomial
degree of a polynomial
like terms
negative of a polynomial5.3
polynomial function
composition of functions
identity function
squaring function
cubing functionKEY TERMS
1 ƒg 21 x 2 ƒ 1 g 1 x 22 composite function
NEW SYMBOLS
SUMMARY
CHAPTER 5
60.Concept Check Let and. Use division
to find polynomials and such that
P 1 x 2 =Q 1 x 2 #D 1 x 2 +R 1 x 2.Q 1 x 2 R 1 x 2P 1 x 2 = 4 x^3 - 8 x^2 + 13 x- 2 D 1 x 2 = 2 x- 1