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

188 Chapter 2 Polynomial and Rational Functions
8.
10.
12.
16.
f x x 3 4x 2 4x 16
Possible rational zeros: ±1, ±2, ±4, ±8, ±16
Zeros shown on graph: 2, 2, 4
Possible rational zeros:
Zeros shown on graph: 1, 1
±1, ±2, ±
1
2 , 2 , 1, 2
1
f x 4x
1
2 , ± 4
5 8x 4 5x 3 10x 2 x 2
f x x 3 7x 6 13.
Possible rational zeros: ±1, ±2, ±3, ±6
3 1
1
14. hx x 3 9x 2 20x 12
Possible rational zeros: ±1, ±2, ±3, ±4, ±6, ±12
1 1
1
hx x 1x 2 8x 12
Thus, the rational zeros are 1, 2, 6.
px x 3 9x 2 27x 27
Possible rational zeros: ±1, ±3, ±9, ±27
3 1
x 1x 2x 6
1
0
3
3
9
1
8
9
3
6
7
9
2
20
8
12
27
18
f x x 3x 2 6x 9
x 3x 3x 3
Thus, the rational zero is 3.
9
6
6
0
f x x 3x 2 3x 2 x 3x 2x 1
Thus, the rational zeros are 2, 1, 3.
12
12
0
27
27
0
9.
11.
15. ht t3 12t2 21t 10
17.
fx 2x 4 17x 3 35x 2 9x 45
Possible rational zeros:
Zeros shown on graph: 1, 3
2 , 3, 5
fx x 3 6x 2 11x 6
Possible rational zeros: ±1, ±2, ±3, ±6
1 1
1
x 3 6x 2 11x 6 x 1x 2 5x 6
Thus, the rational zeros are 1, 2, and 3.
Possible rational zeros: ±1, ±2, ±5, ±10
1 1
1
t 3 12t 2 21t 10 t 1t 2 11t 10
Thus, the rational zeros are 1 and 10.
Cx 2x 3 3x 2 1
Possible rational zeros:
1 2
2
6
1
5
12
1
11
3
2
1
11
5
6
21
11
10
0
1
1
±1, ±3, ±5, ±9, ±15, ±45,
± 1 3 5 9 15 45
2 , ± 2 , ± 2 , ± 2 , ± 2 , ± 2
6
6
0
x 1x 2x 3
gx x 3 4x 2 x 4 x 2 x 4 1x 4
x 4x 2 1
x 4x 1x 1
Thus, the rational zeros of gx are 4 and ±1.
10
10
0
t 1t 1t 10
t 1 2 t 10
±1, ± 1
2
1
1
0
2x 3 3x 2 1 x 12x 2 x 1
x 1x 12x 1
x 1 2 2x 1
Thus, the rational zeros are and 1
2 . 1