C Challenge

63. Reasoning Divide. Look for patterns in your answers.

    1. ( x 2 − 1 ) ÷ ( x − 1 ) open , x squared , minus 1 close divides open x minus 1 close
    2. ( x 3 − 1 ) ÷ ( x − 1 ) open , x cubed , minus 1 close divides open x minus 1 close
    3. ( x 4 − 1 ) ÷ ( x − 1 ) open , x to the fourth , minus 1 close divides open x minus 1 close
    4. Using the patterns, factor x 5 − 1 . x to the fifth , minus 1 .
64. Reasoning The remainder from the division of the polynomial x 3 + a x 2 + 2 a x + 5  by  x + 1  is  3 . x cubed , plus eh , x squared , plus 2 eh x plus 5 , by , x plus 1 , is , 3 .  Find a.
65. Use synthetic division to find ( x 2 + 4 ) ÷ ( x − 2 i ) . open , x squared , plus 4 close divides open x minus 2 i close .
66. Writing Suppose 3, − 2 , negative 2 comma  and 5 are zeros of a cubic polynomial function f(x). What is the sign of f ( 1 ) · f ( 4 ) ? f open 1 close middle dot f open 4 close question mark  (Hint: Sketch the graph; consider all possibilities.)

Standardized Test Prep

SAT/ACT

67. What is the remainder when x 2 − 5 x + 7 x squared , minus 5 x plus 7  is divided by x + 1 ? x plus 1 question mark
    1. 1
    2. 3
    3. 11
    4. 13

68. What is the least degree of a polynomial that has a zero of multiplicity 3 at 1, a zero of multiplicity 1 at 0, and a zero of multiplicity 2 at 2?

    6. 3
    7. 4
    8. 5
    9. 6

69. The equation y = 0 . 17 x y equals 0 . 17 x  represents your weight, on the Moon y in relation to your weight on Earth x. If Al weighs 130 lb on Earth, what would he weigh on the Moon?

    1. 22.1 lb
    2. 92.3 lb
    3. 130 lb
    4. 764.7 lb

    Extended Response

70. The formula for the area of a circle is A = π r 2 . eh equals pi , r squared , .  Solve the equation for r. If the area of a circle is 78 . 5  cm 2 , 78 . 5 , cm squared , comma  what is the radius? Use 3.14 for π . pi .

Mixed Review

See Lesson 5-3.

Find the real solutions of each equation by factoring.

71. x 3 + 2 x 2 + x = 0 x cubed , plus 2 , x squared , plus x equals 0
72. 2 x 4 − 2 x 3 + 2 x 2 = 2 x 2 x to the fourth , minus , 2 x cubed , plus , 2 x squared , equals 2 x
73. 5 x 5 = 125 x 3 5 x to the fifth , equals . 125 x cubed

See Lesson 4-7.

Solve each equation using the Quadratic Formula.

74. x 2 + 3 x − 2 = 0 x squared , plus 3 x minus 2 equals 0
75. 2 x 2 + 4 x − 4 = 0 2 x squared , plus 4 x minus 4 equals 0
76. 7 x 2 − 2 x − 5 = 0 7 x squared , minus 2 x minus 5 equals 0
77. x 2 − 5 x = − 5 x squared , minus 5 x equals negative 5
78. x 2 − 6 x = − 7 x squared , minus 6 x equals negative 7
79. x 2 + 7 x + 11 = 0 x squared , plus 7 x plus 11 equals 0

See Lesson 3-3.

Find the solution of each system by graphing.

80. { y < 2 x + 3 y > − x left brace . table with 2 rows and 1 column , row1 column 1 , y less than 2 x plus 3 , row2 column 1 , y greater than negative x , end table
81. { y > x − 4 y > 4 − 1 3 x left brace . table with 2 rows and 1 column , row1 column 1 , y greater than x minus 4 , row2 column 1 , y greater than 4 minus , 1 third , x , end table
82. { y < − | x | + 3 y > x + 1 left brace . table with 2 rows and 1 column , row1 column 1 , y less than negative absolute value of x , , plus 3 , row2 column 1 , y greater than x plus 1 , end table

Get Ready! To prepare for Lesson 5-5, do Exercises 83–85.

See Lesson 4-8.

Simplify each expression.

83. ( − 4 i ) ( 6 i ) open negative 4 i close open 6 i close
84. ( 2 + i ) ( 2 − i ) open 2 plus i close open 2 minus i close
85. ( 4 − 3 i ) ( 5 + i ) open 4 minus 3 i close open 5 plus i close

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