Factor each expression.

49. x 2 + 27 x + 50 x squared , plus 27 x plus 50
50. g 2 − 18 g + 45 g squared , minus 18 g plus 45
51. k 2 − 18 k − 63 k squared , minus 18 k minus 63
52. d 2 + 30 d − 64 d squared , plus 30 d minus 64
53. s 2 − 10 s t − 75 t 2 s squared , minus 10 s t minus 75 , t squared
54. h 2 + 9 h j − 90 j 2 h squared , plus 9 h j minus 90 , j squared

C Challenge

Factor each trinomial.

Sample

n 6 + n 3 − 42 = ( n 3 ) 2 + n 3 − 42   = ( n 3 − 6 ) ( n 3 + 7 ) table with 2 rows and 3 columns , row1 column 1 , n to the sixth , plus , n cubed , minus 42 , column 2 equals , column 3 open , n cubed , close squared . plus , n cubed , minus 42 , row2 column 1 , , column 2 equals , column 3 open , n cubed , minus 6 close open , n cubed , plus 7 close , end table

55. x 12 + 12 x 6 + 35 x to the twelfth , plus 12 , x to the sixth , plus 35
56. t 8 + 5 t 4 − 24 t to the eighth , plus 5 , t to the fourth , minus 24
57. r 6 − 21 r 3 + 80 r to the sixth , minus 21 , r cubed , plus 80
58. m 10 + 18 m 5 + 17 m to the tenth , plus 18 , m to the fifth , plus 17
59. x 12 − 19 x 6 − 120 x to the twelfth , minus 19 , x to the sixth , minus 120
60. p 6 + 14 p 3 − 72 p to the sixth , plus 14 , p cubed , minus 72

Standardized Test Prep

SAT/ACT

61. What is the factored form of x 2 + x − 42 ? x squared , plus x minus 42 question mark

    1. ( x − 7 ) ( x − 6 ) open x minus 7 close open x minus 6 close
    2. ( x − 7 ) ( x + 6 ) open x minus 7 close open x plus 6 close
    3. ( x + 7 ) ( x − 6 ) open x plus 7 close open x minus 6 close
    4. ( x + 7 ) ( x + 6 ) open x plus 7 close open x plus 6 close

62. What is the solution of the equation 6 x + 7 = 25 ? 6 x plus 7 equals 25 question mark

    6. 2
    7. 3
    8. 5 1 3 5 , and 1 third
    9. 8

63. A museum charges an admission price of $12 per person when you buy tickets online. There is also a $5 charge per order. You spend $65 purchasing p tickets online. Which equation best represents this situation?

    1. 12 p + 5 = 65 12 p plus 5 equals 65
    2. 5 p + 12 = 65 5 p plus 12 equals 65
    3. 12 p − 5 = 65 12 p minus 5 equals 65
    4. 65 p + 12 = 5 65 p plus 12 equals 5

Short Response

64. You and your friend bike to school at the rates shown. Who is faster? Show your work.

You: 7 mi/h

Your friend: 11 ft/s

Mixed Review

See Lesson 8-4.

Simplify each product.

65. ( c + 4 ) 2 open c plus 4 close squared
66. ( 2 v − 9 ) 2 open 2 v minus 9 close squared
67. ( 3 w + 7 ) ( 3 w − 7 ) open 3 w plus 7 close open 3 w minus 7 close

See Lesson 2-5.

Solve each equation for x.

68. a b = x d eh over b , equals , x over d
69. 8 ( x − d ) = x 8 open x minus d close equals x
70. m = ( c + x ) n m equals . fraction open , c plus x , close , over n end fraction

Get Ready! To prepare for Lesson 8-6, do Exercises 71–73.

See Lesson 8-2.

Find the GCF of the terms of each polynomial.

71. 14 x 2 + 7 x 14 , x squared , plus 7 x
72. 24 x 2 − 30 x + 12 24 , x squared , minus 30 x plus 12
73. 6 x 3 + 45 x 2 + 15 6 , x cubed , plus 45 , x squared , plus 15

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