Factor each expression.

38. 54 x 2 + 87 x + 28 54 x squared , plus 87 x plus 28
39. 66 k 2 + 57 k + 12 66 k squared , plus 57 k plus 12
40. 14 z 2 − 53 z + 14 14 z squared , minus 53 z plus 14
41. 28 h 2 + 28 h − 56 28 h squared , plus 28 h minus 56
42. 21 y 2 + 72 y − 48 21 y squared , plus 72 y minus 48
43. 55 n 2 − 52 n + 12 55 n squared , minus 52 n plus 12
44. 36 p 2 + 114 p − 20 36 p squared , plus 114 p minus 20
45. 63 g 2 − 89 g + 30 63 g squared , minus 89 g plus 30
46. 99 v 2 − 92 v + 9 99 v squared , minus 92 v plus 9
47. Reasoning If a and c in a x 2 + b x + c eh x squared , plus b x plus c  are prime numbers and the trinomial is factorable, how many positive values are possible for b? Explain your reasoning.

C Challenge

Factor each expression.

48. 56 x 3 + 43 x 2 + 5 x 56 x cubed , plus , 43 x squared , plus 5 x
49. 49 p 2 + 63 p q − 36 q 2 49 p squared , plus 63 p q minus , 36 q squared
50. 108 g 2 h − 162 g h + 54 h 108 g squared . h minus 162 g h plus 54 h

51. The graph of the function y = x 2 + 5 x + 6 y equals , x squared , plus 5 x plus 6  is shown below.

    1. What are the x-intercepts?
    2. Factor x 2 + 5 x + 6 . x squared , plus 5 x plus 6 .

    3. Reasoning Describe the relationship between the binomial factors you found in part (b) and the x-intercepts.

       

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

52. What is the missing value in the statement 7 x 2 − 61 x − 18 = ( 7 x + 2 ) ( x −   ) ? 7 x squared , minus 61 x minus 18 equals open 7 x plus 2 close open x minus begin box , , end box close question mark
53. What is the y-intercept of the graph of − 3 x + y = 1 ? negative 3 x plus y equals 1 question mark
54. What is the absolute value of the negative solution of the equation | x + 4 | = 9 ? vertical line x plus 4 vertical line equals 9 question mark
55. A book has a spine 4.3 × 10 − 2 4.3 times , 10 super negative 2 end super  m thick. What is 4.3 × 10 − 2 4.3 times , 10 super negative 2 end super  written in standard form?
56. The number of tourists who visit a certain country is expected to be 440% greater in the year 2020 than in the year 2000. What is 440% written as a decimal?

Mixed Review

See Lesson 8-5.

Factor each expression. Check your answer.

57. w 2 + 15 w + 44 w squared , plus 15 w plus 44
58. t 2 − 3 t − 28 t squared , minus 3 t minus 28
59. x 2 − 17 x + 60 x squared , minus 17 x plus 60

See Lesson 2-7.

Solve each proportion.

60. 5 6 = x 15 5 sixths , equals , x over 15
61. 2 3 = d 18 2 thirds , equals , d over 18
62. 5 8 = a 60 5 eighths , equals , eh over 60
63. 6 10 = z 35 6 tenths , equals , z over 35

Get Ready! To prepare for Lesson 8-7, do Exercises 64–67.

See Lesson 8-4.

Simplify each product.

64. ( a + 9 ) 2 open eh plus 9 close squared
65. ( q − 15 ) 2 open q minus 15 close squared
66. ( h − 10 ) ( h + 10 ) open h minus 10 close open h plus 10 close
67. ( 2 x − 7 ) ( 2 x + 7 ) open 2 x minus 7 close open 2 x plus 7 close

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