,-
66
Practice Exercises
~
factor.
In Exercises I-lO,factor
1. 18x
3. 3x2
+ 27
+ 6x
5. 9x4
-
18x3
+
27x2
+ 5) + 3(x + 5)
x2(X - 3) + 12(x - 3)
7. x(x
11. x3
-
13. x3
-
+ 5x - 10
x2 + 2x - 2
2X2 - 6x + 4
2X2
15. 3x3
-
out the greatest common
75. x3
-
76. 9x3
77. x2
+ 64
+ 2x2
6. 6x4
+ 12x2
+ 1) + 4(2x + 1)
+ 5) + 17(2x + 5)
18x3
-
8. x(2x
10. x2(2x
-
14. x3
+
3x2 + 4x - 12
6x2 - 2x - 12
16. ' x3
...:.
X2 - 5x
+
+
29. 4x2 + 16x + 15
. 31. 9x2 - 9x + 2
33. 20x2 + 27x - 8
35. 2x2 + 3xy + i
37. 6x2 - 5xy - 6i
+5
41. 36x2 - 49
43. 9x2 - 25i
X4
81
-
+
45
+
5x - 3
-
2x - 5
+
+ 1
51. x2 - 14x + 49
53. 4x2 + 4x + 1
55. 9x2 - 6x + 1
2x
x3
28. 6x2
-
17x
30. 8x2
+
+
33x
32. 9x2
+
+
of two squares.
48. 81x4
50. x2
+
52. x2 54. 25x2
56. 64x2
+4
lOx + 25
+ lOx + 1
- 16x + 1
4x
+
64
64
60. x3
-
27
+
27
62. 27x3
64. 8x3
In Exercises 65-92, factor completely,
is prime.
65. 3x3
-
3x
67. 4x2 - 4x - 24
92.
2x3
-
8a2 x
i - 16y
-
98a2 x
X -
2
+
2S - 361
- 3i
86. x2 - lOx
9b2y
+
16a2y
+
32 - 2x2 90. 12x2y - 27y - 4x2
+
24x2
+
28x2
+
+
9
72x
+
98x
t
3
3
93. x2 - X2
t
3
t
+
96. 12x -4
3
+ 3)2 -
99. (x
+ 5f2 - (x + 5f2
(x
6x4
3
97. (x
+ 3)2
7
+ 4)2 + (x2 + 4)2
98. (x2
1
3
2
100.
t
94. x4 - x4
5
(x2 + 3)-3 + (x2 +'3)-3
1
-
.
t
3
-
101. (4x - 1)2 - 3'(4x - 1)2
102. -8(4x
+
3r
2
+
1O(5x
In Exercises 103-114,factor
1
-
-
63. 64x3
+
89. x2y - 16y
91.
82.
-
+
3r
t
+
1)(4x
40. x2 - 144
42. 64x2 - 81
44. 36x2 - 49i
58. x3
1
+ 36 - 49 i
88. 16a2x - 25y - 25x
2x3
80.
x3
84. 48/
87. 9b2x - 16y - 16x
4
34. 15x2 - 19x + 6
36. 3x2 + 4xy + i
38. 6x2 - txy - 5i
27
-
45i
1
12
5x - 4
+
61. 8x3
i - 81y
- 4x - 8
2
In Exercises 57-64, factor using the formula for the sum or difference of two cubes.
57. x3
81.
83. 2ol-
+ 36
+ 2x2
78. x2
95. 4x -3 + 8x3
In Exercises 49-56, factor each perfect square trinomial.
49. x2
79.
x3
9x
-
In Exercises 93-102, factor and simplify each algebraic expression.
46. x4 - 1
16
-
47. 16x4
15
3x2
24. 2x2
In Exercises 39-48, factor the difference
39. x2 - 100
8x
22. x2 - 14x
26.
4x
85. X2 - 12x
12. x3
20. x2 - 4x - 5
23. 3x2 - x - 2
25. 3x2 - 25x - 28
27. 6x2 - 11x + 4
I
.,
3x2 - 25x - 75
4. 4x2 - 8x
19. X2 - 2x - 15
59.
"0"
7
-
+
72. x3
2x2 - 9x - 18
2. 16x - 24
18. X2
15
+
74. 6x2 - 6x - 12
17. x2 + 5x + 6
+
71.
x3
73. 2x2 - 2x - 112
In Exercises 17-38, factor each trinomial, or state that the trinomial
is prime.
21. x2 - 8x
70. 7x4
69. 2X4 - 162
In Exercises 11-16, factor by grouping.
45.
-
Chapter P • Prerequisites: Fundamental Concepts of Algebra
-.-.~
9.
,.-.
-
+
103. 10x2(x
104. 12x2(x
105.
6x4
107. /
+
+
1) - 7x(x
- 1) - 4x(x
3Sx2 "-'..6
+ Y
109. x4 - 5x21
completely.
+
106. 7 X4
+
3/
+
+
34x2
1)3
+
110. x4 - 10x21
111. (x - y)4 - 4(x - y)2 112. (x
113. 2x2 - txl
1)
- 1) - 5(x - 1)
108. (y
+ 4/
+
1) - 6(x
114. 3x2
+
5
-
1
+ 9/
y)4 - 100(x
+
5xi
+
+
y)2
2l
7
1
125
or state that the polynomial
66. 5x3 - 45x
68. 6x2 - 18x - 60
"'" Application Exercises
115. Your computer store is having an incredible sale. The price
on one model is reduced by 40%. Then the sale price is
reduced by another 40%. If x is the computer's
original
price, the sale price can be represented by
(x - O.4x) - O.4(x - O.4x).
'*Aii,;;