43. 44.
45. 46.
47. 48.
49. 50.
51. 52.
53. 54.
55. 56.
57. 58.
59. 60.
61. 62.
63. 64.
65. 66.
67. 68.
69. 70.
71. 72.
73. 74.
75. 76.
77. 78.
If a trinomial has a negative coefficient for the squared term, as in , it is
usually easier to factor by first factoring out the common factor
Use this method to factor each trinomial. See Example 7( b).
Brain Busters Factor each polynomial. (Hint:As the first step, factor out the greatest com-
mon factor.)
85.
86.
87.
88.
Brain Busters Find all integers k so that the trinomial can be factored by the methods of
this section.
- 2 m^2 +km+ 5 92. 3 y^2 +ky+ 4
5 x^2 +kx- 1 2 x^2 +kx- 3
4 t^21 k+ 927 + 20 ts 1 k+ 927 + 25 s^21 k+ 927
9 x^21 r+ 323 + 12 xy 1 r+ 323 + 4 y^21 r+ 323
18 x^21 y- 322 - 21 x 1 y- 322 - 41 y- 322
25 q^21 m+ 123 - 5 q 1 m+ 123 - 21 m+ 123
- 2 a^2 - 5 ab- 2 b^2 - 3 p^2 + 13 pq- 4 q^2
- 3 x^2 - x+ 4 - 5 x^2 + 2 x+ 16
- x^2 - 4 x+ 21 - x^2 +x+ 72
=- 112 x- 321 x- 42
=- 112 x^2 - 11 x+ 122
- 1.
24 x^2 + 38 xy+ 15 y^224 x^2 + 62 xy+ 33 y^2
24 x^4 + 55 x^2 - 24 24 x^4 + 17 x^2 - 20
24 x^2 - 46 x+ 15 24 x^2 - 94 x+ 35
36 a^3 b^2 - 104 a^2 b^2 - 12 ab^236 p^4 q+ 129 p^3 q- 60 p^2 q
10 x^4 y^5 + 39 x^3 y^5 - 4 x^2 y^514 x^7 y^4 - 31 x^6 y^4 + 6 x^5 y^4
48 a^2 - 94 ab- 4 b^248 t^2 - 147 ts+ 9 s^2
36 x^4 - 64 x^2 y+ 15 y^236 x^4 + 59 x^2 y+ 24 y^2
24 y^2 - 41 xy- 14 x^224 x^2 + 19 xy- 5 y^2
12 x^2 - 47 x- 4 12 x^2 - 19 x- 10
- 10 x^3 + 5 x^2 + 140 x - 18 k^3 - 48 k^2 + 66 k
16 + 16 x+ 3 x^218 + 65 x+ 7 x^2
5 - 6 x+x^27 - 8 x+x^2
6 m^6 n+ 7 m^5 n^2 + 2 m^4 n^312 k^3 q^4 - 4 k^2 q^5 - kq^6
12 s^2 + 11 st- 5 t^225 a^2 + 25 ab+ 6 b^2
5 a^2 - 7 ab- 6 b^26 x^2 - 5 xy-y^2
15 x^2 y^2 - 7 xy^2 - 4 y^214 a^2 b^3 + 15 ab^3 - 9 b^3
15 n^4 - 39 n^3 + 18 n^224 a^4 + 10 a^3 - 4 a^2
40 m^2 q+mq- 6 q 15 a^2 b+ 22 ab+ 8 b
380 CHAPTER 6 Factoring and Applications
Find each product. See Section 5.6.
- 1 x+ 622 96. 13 t+ 422
17 p+ 3217 p- 32 13 h+ 5 k 213 h- 5 k 2
PREVIEW EXERCISES
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