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

58. f x 3x Factors: x 3, x 2
3 2x2 19x 6;
(a)
3 3
3
2 3
3
2
9
7
7
6
1
2
2
19
21
(b) The remaining factor is 3x 1.
(b)
4 1
1
1
4
3
0
2
10
12
2
6
6
59. f x x Factors:
(a) 5 1 4 15 58 40
5 5 50 40
1 1 10 8 0
4 4x3 15x2 58x 40;
Both are factors of since the remainders are zero.
x
The remaining factors are x 1 and x 2.
2 f x
3x 2 x 1x 2
0
8
8
0
x 5, x 4
60. f x 8x Factors: x 2, x 4
4 14x3 71x2 10x 24;
(a)
2 8
4 8
8
8
14
16
30
30
32
2
71
60
11
11
8
3
10
22
12
12
(b) 8x
The remaining factors are 4x 3 and 2x 1.
2 2x 3 4x 32x 1
0
12
61. Factors:
(a) 1
f x 6x
2 6 41 9 14
3 19 14
6 38 28 0
3 41x2 9x 14;
2
3
6
6
38
4
42
28
28
0
24
24
Both are factors since the remainders are zero.
(c) f x x 72x 13x 2
0
2x 1, 3x 2
Section 2.3 Polynomial and Synthetic Division 175
(c)
(d) Zeros:
(e)
(c)
−4 3
(c)
(d) Zeros:
(e)
f x 3x 3 2x 2 19x 6
(d) Zeros:
3x 1x 3x 2
1
3, 3, 2
35
−10
f x x 1x 2x 5x 4
1, 2, 5, 4
20
−6 6
−180
f x 4x 32x 1x 2x 4
3
4, 1
2, 2, 4
(e) 40
−3 5
−380
(b)
f x
This shows that
x
f x
so
x 7.
2x 13x 2
The remaining factor is x 7.
1
2x 2
6x 42 6x 7
6x 7,
3
(d) Zeros:
(e)
7, 1 2
,
2 3
320
−9 3
−40