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

190 Chapter 2 Polynomial and Rational Functions
24.
26.
28.
30.
x 5 x 4 3x 3 5x 2 2x 0
xx 4 x 3 3x 2 5x 2 0
Possible rational zeros of x
±1, ±2
4 x3 3x2 5x 2:
1 1
f x 4x 3 12x 2 x 15
(a) Possible rational zeros:
(b)
15
12
−9 −6 −3 6 9 12
(c) Real zeros: 1, 3 5
2 , 2
f x 4x 4 17x 2 4
(a) Possible rational zeros:
(b)
1
2 1
1
1
1
0
0
2
2
xx 1x 2x 2 2x 1 0
xx 1x 2x 1x 1 0
The real zeros are 2, 0, 1.
(c) Real zeros: ±2, ± 1
2
y
3
0
3
−8 8
9
−15
3
4
1
5
3
2
2
2
0
2
2
0
± 5
±1, ±3, ±5, ±15, ±
15 1 3 5 15
2 , ± 2 , ± 4 , ± 4 , ± 4 , ± 4
1 3
2 , ± 2 ,
x
±1, ±2, ±4, ± 1 1
2 , ± 4
25.
29.
fx x 3 x 2 4x 4
(a) Possible rational zeros:
(b)
(c) The zeros are: 2, 1, 2
fx 2x 4 13x 3 21x 2 2x 8
(a) Possible rational zeros:
(b)
16
−4 8
−8
(c) The zeros are: 1
2 , 1, 2, 4
31. fx 32x
(a) Possible rational zeros:
3 52x2 17x 3
(b)
−6 −4 4 6
f x 3x 3 20x 2 36x 16 27. fx 4x3 15x2 8x 3
(a) Possible rational zeros:
(b)
10
8
6
4
2
−4 −2 6 8 10 12
−4
−6
y
(c) Real zeros: 2
3 , 2, 4
± 2
±1, ±2, ±4, ±8, ±16, ±
4 8 16
3 , ± 3 , ± 3 , ± 3
1
3 ,
x
6
−1 3
−2
4
2
−4
−6
−8
(a) Possible rational zeros:
(b)
4
2
(c) The zeros are: 1
8, 3
4, 1
y
−6 −4 −2 2 4 6 8 10
−4
−6
y
(c) The zeros are: 1
4 , 1, 3
±1, ±2, ±4
x
±1, ±3, ± 1
2, ± 3
2, ± 1
4, ± 3
4
x
±1, ±2, ±4, ±8, ± 1
2
± 1
±1, ±3, ±
3 1 3 1 3
6 , ± 8 , ± 16 , ± 16 , ± 32 , ± 32
1 3 1 3
2 , ± 2 , ± 4 , ± 4 ,