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

58. f x 3x
(a) 4 3 8 20 16
12 16 16
3 4 4 0
3 8x2 20x 16
59.
Yes, x 4 is a zero of f.
(c)
2
3 3 8 20 16
2 4 16
3 6 24 0
f x x 4 10x 3 24x 2 20x 44
(a)
Yes, x is a zero of f.
2
3
3 1
1
10
3
7
24
21
45
Thus, f 3 421.
Thus, g2 0.
20
135
155
60. gt 2t
(a) 4 2 5 0 0
8 52 208
2 13 52 208
Thus, g4 3276.
(b) 2 2 5
22
2 5 22
5 5t4 8t 20
(e)
80
−8 5
−60
44
465
421
8
832
824
0
52 4
52 4
20
3296
3276
0
10 42
10 42
(b)
(b)
4 3
1 1
1
3
f 1 9
10
1
9
Review Exercises for Chapter 2 245
8
12
20
No, x 4 is not a zero of f.
(d) 1 3 8 20 16
3 11 9
3 11 9 25
8
102 8
102
No, x 1 is not a zero of f.
20
20
0
24
9
33
20
80
60
20
33
53
16
240
224
61. ; Factor:
(a)
Yes, is a factor of
(b)
The remaining factors of are and
(c) f x x
x 7x 1x 4
(d) Zeros: 7, 1, 4
3 4x2 x
f x 7 x 1.
25x 28
2 f x x x 4
4 1 4 25 28
4 32 28
1 8 7 0
x 4
f x.
8x 7 x 7x 1
3 4x2 25x 28 62.
(a)
Yes, is a factor of
(b)
The remaining factors are and
(c)
(d) Zeros: x
(e)
50
5
2x
2x 5 x 3.
f x 2x 5x 3x 6
2 , 3, 6
2 f x 2x
6 2 11 21 90
12 6 90
2 1 15 0
x 6
f x.
x 15 2x 5x 3
3 11x2 21x 90
−7 5
−100
44
53
9