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

246 Chapter 2 Polynomial and Rational Functions
63. f x x
Factors: x 2, x 3
(a) 2 1
4 4x3 7x2 22x 24 64. f x x
(a) 2 1 11 41 61 30
1
2
9
18
23
46
15
30
0
4 11x3 41x2 61x 30
(b)
(c)
(d) Zeros:
(e)
Both are factors since the remainders are zero.
x
The remaining factors are x 1 and x 4.
2 3 1 6 5 12
3 9 12
1 3 4 0
3x 4 x 1x 4
f x x 1x 4x 2x 3
−3
1
2, 1, 3, 4
40
−10
4
2
6
7
12
5
5
22
10
12
24
24
0
(b)
Yes, and are both factors of
x
The remaining factors are x 1 and x 3.
2 5 1 9 23 15
5 20 15
1 4 3 0
x 2 x 5
f x.
4x 3 x 1x 3
(c)
(d) Zeros:
(e)
f x x 1x 3x 2x 5
x 1, 2, 3, 5
4
−6 12
65. 6 4 6 2i 66. 3 25 3 5i 67. i 2 3i 1 3i
68. 5i i 2 1 5i 69. 7 5i 4 2i 7 4 5i 2i 3 7i
70. 2 2
2 2 2 2 2 2 2 2 2
i i i
2 2 2 2 2 2 2 2 i
−8
i 2i
71. 5i13 8i 65i 40i2 40 65i 72. 1 6i5 2i 5 2i 30i 12i2 73.
75.
4 46i
5 28i 12
17 28i
10 8i2 3i 20 30i 16i 24i2 74. i6 i3 2i i18 12i 3i 2i2 6 i 6 i 4 i
4 i 4 i 4 i
24 10i i2
16 1
23 10i
17
23 10
17 17 i
76.
17 7i
26
17 7i
26 26
i20 9i
20i 9i 2
9 20i
3 2i 3 2i 5 i
5 i 5 i 5 i
15 3i 10i 2i2
25 i 2