C Challenge

55. Simplify x 16 − 1 x − 1 fraction x to the sixteenth , minus 1 , over x minus 1 end fraction  by long division and by factoring. Which method do you prefer? Explain your answer.

Divide.

56. ( 4 a 3 b 4 − 6 a 2 b 5 + 10 a 2 b 4 ) ÷ 2 a b 2 open 4 , eh cubed , b to the fourth , minus 6 , eh squared , b to the fifth , plus 10 , eh squared , b to the fourth , close divides 2 eh , b squared
57. ( 15 x 2 + 7 x y − 2 y 2 ) ÷ ( 5 x − y ) open 15 , x squared , plus 7 x y minus 2 , y squared , close divides open 5 x minus y close
58. ( 90 r 6 + 28 r 5 + 45 r 3 + 2 r 4 + 5 r 2 ) ÷ ( 9 r + 1 ) open 90 , r to the sixth , plus 28 , r to the fifth , plus 45 , r cubed , plus 2 , r to the fourth , plus 5 , r squared , close divides open 9 r plus 1 close
59. ( 2 b 6 + 2 b 5 − 4 b 4 + b 3 + 8 b 2 − 3 ) ÷ ( b 3 + 2 b 2 − 1 ) open 2 , b to the sixth , plus 2 , b to the fifth , minus 4 , b to the fourth , plus , b cubed , plus 8 , b squared , minus 3 close divides open , b cubed , plus 2 , b squared , minus 1 close

Standardized Test Prep

SAT/ACT

60. Which of the following is true for ( 2 x 2 + 4 x + 2 ) ÷ 2 x ? open 2 , x squared , plus 4 x plus 2 close divides 2 x question mark
    1. The remainder is negative.
    2. The dividend is in standard form.
    3. The quotient is greater than the divisor for positive values of x.
       1. I only
       2. II only
       3. I and II
       4. II and III
61. Which equation represents the line that passes through (5, − 8 negative 8 ) and is parallel to the line below?

    

    6. y = 2 x + 2 y equals 2 x plus 2
    7. y + 2 x = 2 y plus 2 x equals 2
    8. y = − 2 x y equals negative 2 x
    9. y − 2 x = 2 y minus 2 x equals 2
62. What are the factors of the expression x 3 − 4 x ? x cubed , minus 4 x question mark
    1. x 3 , − 4 x x cubed , comma negative 4 x
    2. x , x 2 − 4 x comma , x squared , minus 4
    3. x − 2 , x + 2 x minus 2 comma x plus 2
    4. x , x − 2 , x + 2 x comma x minus 2 comma x plus 2

Short Response

63. A theater has 18 rows of seats. Each row has 28 seats. Tickets cost $4 for adults and $2.50 for children. The Friday night show was sold out and the revenue from ticket sales was $1935. Barbara says that 445 adults were at the show. Is her statement reasonable? Explain your answer.

Mixed Review

See Lesson 11-2.

Multiply or divide.

64. n 2 + 7 n − 8 n − 1 ⋅ n 2 − 4 n 2 + 6 n − 16 fraction n squared , plus 7 n minus 8 , over n minus 1 end fraction . dot . fraction n squared , minus 4 , over n squared , plus 6 n minus 16 end fraction
65. 6 t 2 − 30 t 2 t 2 − 53 t − 55 ⋅ 6 t 2 + 35 t + 11 18 t 2 fraction 6 , t squared , minus 30 t , over 2 , t squared , minus 53 t minus 55 end fraction . dot . fraction 6 , t squared , plus 35 t plus 11 , over 18 , t squared end fraction
66. 3 c 2 − 4 c − 32 2 c 2 + 17 c + 35 ÷ c − 4 c + 5 fraction 3 , c squared , minus 4 c minus 32 , over 2 , c squared , plus 17 c plus 35 end fraction . divides . fraction c minus 4 , over c plus 5 end fraction
67. x 2 + 9 x + 20 x 2 + 5 x − 24 ÷ x 2 + 15 x + 56 x 2 + x − 12 fraction x squared , plus 9 x plus 20 , over x squared , plus 5 x minus 24 end fraction . divides . fraction x squared , plus 15 x plus 56 , over x squared , plus x minus 12 end fraction

Get Ready! To prepare for Lesson 11-4, do Exercises 68–71.

See Lesson 1-5.

Simplify each expression.

68. 4 9 + 2 9 4 ninths , plus , 2 ninths
69. 1 4 − 1 3 1 fourth , minus , 1 third
70. 7 x 8 + x 8 fraction 7 x , over 8 end fraction , plus , x over 8
71. 7 12 y − 1 12 y fraction 7 , over 12 y end fraction , minus , fraction 1 , over 12 y end fraction

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