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

79.
83.
x n 3 ) x 3n 9x 2n 27x n 27
x 3n 9x 2n 27x n 27
x n 3
5 1
1
x 3n 3x 2n
4
5
9
6x 2n 27x n
6x 2n 18x n
3
45
42
x 2n 6x n 9
9x n 27
9x n 27
c
210
c 210
x 2n 6x n 9
81. A divisor divides evenly into a dividend if the remainder
is zero.
85.
87.
89.
To divide evenly, c 210 must equal zero. Thus, c must
equal 210.
fx x 3 2 x 3x 1 3
The remainder when k 3 is zero since x 3
is a factor of fx.
9x 2 25 0
3x 53x 5 0
5x 2 3x 14 0
5x 7x 2 0
91. 2 x2 6x 3 0
0
3x 5 0 ⇒ x 5
3
3x 5 0 ⇒ x 5
3
5x 7 0 ⇒ x 7
5
x 2 0 ⇒ x 2
x b ± b2 4ac
2a
3 ± 3
2
6 ± 62 423
22
Section 2.3 Polynomial and Synthetic Division 179
80.
x n 2 ) x 3n 3x 2n 5x n 6
x 3n 2x 2n
x 2n 5x n
x 2n 2x n
x 3n 3x 2n 5x n 6
x n 2
x 2n x n 3
3 x n 6
3 x n 6
0
x 2n x n 3
82. You can check polynomial division by multiplying the
quotient by the divisor. This should yield the original
dividend if the multiplication was performed correctly.
84.
2 1
0
2
0
4
2
8
1
20
c
42
1 2 4 10 21 c 42
To divide evenly, c 42 must equal zero. Thus, c must
equal 42.
86. In this case it is easier to evaluate f2 directly because
f x is in factored form. To evaluate using synthetic
division you would have to expand each factor and then
multiply it all out.
88. 16x2 21 0
90.
16x 2 21
4x 5 0
x 2 21
16
x 5
4
x ± 21
16
x ± 21
4
8x 2 22x 15 0
4x 52x 3 0
6 ± 12
4
or
or x 3
2x 3 0
2