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

200 Chapter 2 Polynomial and Rational Functions
91.
95.
fx 4x 3 3x 1
Possible rational zeros:
1 4
4
0
4
4
3
4
1
1
1
0
4x 3 3x 1 x 14x 2 4x 1
x 12x 1 2
Thus, the zeros are 1 and 1
2.
93. fy 4y
Possible rational zeros:
3 3y2 8y 6
97.
3
4
4
4
3
3
0
8
0
8
Px x 4 25
4 x2 9
1
44x 4 25x 2 36
1
44x 2 9x 2 4
±1, ± 1 1
2 , ± 4
6
6
0
4y 3 3y 2 8y 6 y 3
44y 2 8
Thus, the only real zero is 3
4 .
y 3
44y 2 2
4y 3y 2 2
1
42x 32x 3x 2x 2
The rational zeros are ± and ±2.
3
2
±1, ±2, ±3, ±6, ± 1 3 1 3
2 , ± 2 , ± 4 , ± 4
f x x 3 1
4 x2 x 1
4 98.
1
44x 3 x 2 4x 1
1
4x 2 4x 1 14x 1
1
44x 1x 2 1
1
44x 1x 1x 1
The rational zeros are 1
4 and ±1.
92.
Possible rational zeros:
3
2
f z 12z 3 4z 2 27z 9
12
12
4
18
14
f z 2z 3
26z 2 7z 3
2z 33z 12z 3
Real zeros: 3
2
27
21
6
1 3
, 3 , 2
± 1
±1, ±3, ±9, ±
3 9 1 1
4 , ± 4 , ± 4 , ± 6 , ± 12
1 3 9 1
2 , ± 2 , ± 2 , ± 3 ,
9
9
0
94. gx 3x3 2x 2 15x 10
96.
Possible rational zeros:
2
3
3
3
2
2
0
15
0
15
10
10
gx x 2
33x 2 15 3x 2x 2 5
Thus, the only real zero is 2
3 .
4 2
2
3
8
5
23
20
3
The rational zeros are 3, 1
2 , and 4.
± 5 10
±1, ±2, ±5, ±10, ± 3 , ± 3
1 2
3 , ± 3 ,
0
f x
Possible rational zeros: ±1, ±2, ±3, ±4, ±6, ±12,
1
22x 3 3x 2 23x 12
12
12
0
± 1 3
2 , ± 2
f x 1
2x 42x 2 5x 3 1
2x 42x 1x 3
f z 1
66z 3 11z 2 3z 2
Possible rational zeros:
2 6
6
11
12
1
3
2
1
2
2
0
f x 1
6x 26x 2 x 1
1
6x 23x 12x 1
Rational zeros: 2, 1 1
3 , 2
±1, ±2, ± 1 1 2 1
2 , ± 3 , ± 3 , ± 6