Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Factor each expression.

14. x 2 + 3 x + 2 x squared , plus 3 x plus 2
15. x 2 + 5 x + 6 x squared , plus 5 x plus 6
16. x 2 + 7 x + 10 x squared , plus 7 x plus 10
17. x 2 + 10 x + 16 x squared , plus 10 x plus 16
18. y 2 + 15 y + 36 y squared , plus 15 y plus 36
19. x 2 + 22 x + 40 x squared , plus 22 x plus 40
20. x 2 − 3 x + 2 x squared , minus 3 x plus 2
21. − x 2 + 13 x − 12 negative , x squared , plus 13 x minus 12
22. − r 2 + 11 r − 18 negative , r squared , plus 11 r minus 18
23. x 2 − 10 x + 24 x squared , minus 10 x plus 24
24. d 2 − 12 d + 27 d squared , minus 12 d plus 27
25. x 2 − 13 x + 36 x squared , minus 13 x plus 36
26. x 2 − 5 x − 14 x squared , minus 5 x minus 14
27. − x 2 − x + 20 negative , x squared , minus x plus 20
28. − x 2 + 3 x + 40 negative , x squared , plus 3 x plus 40
29. c 2 + 2 c − 63 c squared , plus 2 c minus 63
30. x 2 + 10 x − 75 x squared , plus 10 x minus 75
31. − t 2 + 7 t + 44 negative , t squared , plus 7 t plus 44

See Problem 2.

Find the GCF of each expression. Then factor the expression.

32. 3 a 2 + 9 3 eh squared , plus 9
33. 25 b 2 − 20 b 25 b squared , minus 20 b
34. x 2 − 2 x x squared , minus 2 x
35. 5 t 2 − 5 t − 10 5 t squared , minus 5 t minus 10
36. 14 y 2 + 7 y − 21 14 y squared , plus 7 y minus 21
37. 27 p 2 − 9 p + 18 27 p squared , minus 9 p plus 18

See Problems 3–5

Factor each expression.

38. 3 x 2 + 31 x + 36 3 x squared , plus 31 x plus 36
39. 2 x 2 − 19 x + 24 2 x squared , minus 19 x plus 24
40. 5 r 2 + 23 r + 26 5 r squared , plus 23 r plus 26
41. 2 m 2 − 11 m + 15 2 m squared , minus 11 m plus 15
42. 5 t 2 + 28 t + 32 5 t squared , plus 28 t plus 32
43. 2 x 2 − 27 x + 36 2 x squared , minus 27 x plus 36
44. 3 x 2 + 7 x − 20 3 x squared , plus 7 x minus 20
45. 5 y 2 + 12 y − 32 5 y squared , plus 12 y minus 32
46. 7 x 2 − 8 x − 12 7 x squared , minus 8 x minus 12
47. 2 z 2 + z − 28 2 z squared , plus z minus 28
48. 3 x 2 + 8 x − 16 3 x squared , plus 8 x minus 16
49. 28 k 2 + 13 k − 6 28 k squared , plus 13 k minus 6
50. x 2 + 2 x + 1 x squared , plus 2 x plus 1
51. t 2 − 14 t + 49 t squared , minus 14 t plus 49
52. k 2 − 18 k + 81 k squared , minus 18 k plus 81
53. 4 z 2 − 20 z + 25 4 z squared , minus 20 z plus 25
54. 9 x 2 + 48 x + 64 9 x squared , plus 48 x plus 64
55. 81 z 2 + 36 z + 4 81 z squared , plus 36 z plus 4
56. x 2 − 4 x squared , minus 4
57. c 2 − 64 c squared , minus 64
58. 9 x 2 − 1 9 x squared , minus 1

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