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

198 Chapter 2 Polynomial and Rational Functions
75.
78.
fx 16x 3 20x 2 4x 15 76.
Possible rational zeros:
± 5
4, ± 15
4 , ± 1
8, ± 3
8, ± 5
8, ± 15
8 , ± 1
16, ± 3
16, ± 5
16, ± 15
±1, ±3, ±5, ±15, ±
16
1
2, ± 3
2, ± 5
2, ± 15
2 , ± 1
4, ± 3
4,
Based on the graph, try
By the Quadratic Formula, the zeros of
16x are
2 32x 20 44x2 8x 5
x
−3
3
4
8 ± 64 80
8
The zeros of are x 3
fx
−4
16
16
gx x 5 8x 4 28x 3 56x 2 64x 32
Possible rational zeros: ±1, ±2, ±4, ±8, ±16, ±32
10
−10 10
−10
20
−5
20
12
32
−5
x 3
4.
4
24
20
1 ± 1
2 i.
Based on the graph, try x 2.
3
4
4
15
15
0
and x 1 ± 1
2 i.
2 1
2 1
2 1
By the Quadratic Formula, the zeros of x are
2 2x 4
x
1
1
1
f x 9x 3 15x 2 11x 5
Possible rational zeros:
−5 5
Based on the graph, try x 1.
1 9
By the Quadratic Formula, the zeros of 9x are
2 6x 5
x
The zeros of are x 1 and x 1
fx
8
2
6
6
2
4
4
2
2
9
28
12
16
8
8
4
4
2 ± 4 16
2
15
9
6
6 ± 36 180
18
16
8
5
−5
24
16
8
8
8
0
11
6
5
56
32
24
1 ± 3i.
±1, ±5, ± 1 5 1 5
3 , ± 3 , ± 9 , ± 9
5
5
0
1 2
±
3 3 i.
77.
Possible rational zeros: ±1, ±2, ±
20
1
fx 2x
2
4 5x3 4x2 5x 2 Based on the graph, try x 2 and x
2 2 5 4 5 2
2
4
1
2
2
4
1
2
0
1
2 .
1
2
2
2
1
1
0
2
0
2
1
1
0
The zeros of are
The zeros of are x 2, x 1
2x x ±i.
fx
2, and x ±i.
2 2 2x2 1
64
48
16
16
16
The zeros of gx are x 2 and x 1 ± 3i.
0
32
32
0
3
± 2
3i.