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

67.
69.
71.
ht t 3 2t 2 7t 2
(a) The zeros of h are t 2, t 3.732, t 0.268.
(b) An exact zero is t 2.
(c) 2 1 2 7 2
2 8 2
1 4 1 0
x 4 6x 3 11x 2 6x
x 2 3x 2
1 1
1
2 1
ht t 2t 2 4t 1
By the Quadratic Formula, the zeros of t
are 2 ± 3. Thus,
ht t 2t 2 3t 2 3
2 4t 1
1
t 2t 2 3 t 2 3 .
4x 3 8x 2 x 3
2x 3
3
2
4
4
8
6
2
4x 3 8x 2 x 3
x 3
2
Thus, 4x3 8x 2 x 3
2x 3
6
1
5
5
2
3
11
5
6
6
6
0
x 4 6x 3 11x 2 6x
x 1x 2
73. (a) and (b)
1800
3
1200
—CONTINUED—
1
3
2
4x 2 2x 2 22x 2 x 1
13
3
3
0
x4 6x 3 11x 2 6x
x 1x 2
6
6
0
0
0
0
2x 2 x 1, x 3
2 .
0
0
0
x 2 3x, x 2, 1
Section 2.3 Polynomial and Synthetic Division 177
68.
70.
72.
f s s 3 12s 2 40s 24
(a) The zeros of f are s 6, s 0.764, s 5.236
(b) s 6 is an exact zero.
(c) 6 1 12 40 24
6 36 24
1 6 4 0
f s s 6s 2 6s 4
8 1
s 6s 3 5s 3 5
x 3 x 2 64x 64
x 8
1
1
8
7
x 3 x 2 64x 64
x 8
2 1
1
2 1
1
9
2
11
11
2
9
64
56
8
5
22
17
17
18
x 4 9x 3 5x 2 36x 4
x 2 4
64
64
0
x 4 9x 3 5x 2 36x 4
x 2 4
x , x 8
2 7x 8
1
36
34
2
2
2
0
x 4 9x 3 5x 2 36x 4
x 2x 2
4
4
0
x , x ±2
2 9x 1