C H A P T E R 2 Polynomial and Rational Functions

99. fx x
Rational zeros: 1 x 1
Irrational zeros: 0
Matches (d).
3 1 x 1x2 x 1
103. (a)
(c)
9
Volume of box
125
100
75
50
25
V
15
x
x
9 − 2x
1 2 3 4 5
Length of sides of
squares removed
The volume is maximum when x 1.82.
x
15 − 2x
The dimensions are: length 15 21.82 11.36
width 9 21.82 5.36
height x 1.82
1.82 cm 5.36 cm 11.36 cm
x
100.
(b)
(d)
Section 2.5 Zeros of Polynomial Functions 201
f x x 3 2
x 3 2x 2 3 2x 3 4
Rational zeros: 0
Irrational zeros:
Matches (a).
1 x 3 2
101. f x x
Rational zeros: 3 x 0, ±1
Irrational zeros: 0
Matches (b).
3 x xx 1x 1 102.
xx
xx 2x 2
Rational zeros: 1 x 0
Irrational zeros: 2 x ±2
Matches (c).
2 f x x
2
3 2x
104. (a) Combined length and width:
(b)
4x y 120 ⇒ y 120 4x
Volume l w h x 2 y
18,000
0 30
0
Dimensions with maximum volume:
20 in. 20 in. 40 in.
x 2 120 4x
4x 2 30 x
(c)
V l w h 15 2x9 2xx
x9 2x15 2x
Since length, width, and height must be positive,
we have 0 < x < for the domain.
9
56 x9 2x15 2x
56 135x 48x 2 4x 3
50 4x 3 48x 2 135x 56
2
1 7
2 ,
The zeros of this polynomial are 2 , and 8.
x cannot equal 8 since it is not in the domain of V.
[The length cannot equal 1 and the width cannot
equal 7.
The product of 817 56 so it
showed up as an extraneous solution.]
Thus, the volume is 56 cubic centimeters when
centimeter or x centimeters.
7
x 2
1
2
15 1
1
13,500 4x 2 30 x
4x 3 120x 2 13,500 0
x 3 30x 2 3375 0
30
15
15
0
225
225
x 15x 2 15x 225 0
3375
3375
Using the Quadratic Formula, x 15,
15 ± 155
.
2
15 155
The value of is not possible because
2
it is negative.
0