B Apply

59. Think About a Plan Suppose you cut a small square from a square sheet of cardboard. Find the sides of one rectangle whose area is equal to the area of the remaining part.

    

    • How can you represent the remaining part as a combination of rectangles with known sides?
    • Can you factor the resulting expression?
60. The area in square centimeters of a square area rug is 25 x 2 − 10 x + 1 . 25 x squared , minus 10 x plus 1 .  What are the dimensions of the rug in terms of x?

Factor each expression completely.

61. 9 x 2 − 36 9 x squared , minus 36
62. 18 z 2 − 8 18 z squared , minus 8
63. 12 y 2 − 75 12 y squared , minus 75
64. 64 t 2 − 16 64 t squared , minus 16
65. 12 x 2 + 36 x + 27 12 x squared , plus 36 x plus 27
66. 16 x 2 − 80 x + 100 16 x squared , minus 80 x plus 100
67. 2 a 2 − 16 a + 32 2 eh squared , minus 16 eh plus 32
68. 3 x 2 − 24 x − 27 3 x squared , minus 24 x minus 27
69. 18 b 2 + 24 b − 10 18 b squared , plus 24 b minus 10
70. 4 n 2 − 20 n + 24 4 n squared , minus 20 n plus 24
71. 3 y 2 + 24 y + 45 3 y squared , plus 24 y plus 45
72. − x 2 + 5 x − 4 negative , x squared , plus 5 x minus 4
73. 4 x 2 − 22 x + 10 4 x squared , minus 22 x plus 10
74. 1 2 x 2 − 1 2 1 half , x squared , minus , 1 half
75. − 6 z 2 − 600 negative 6 , z squared , minus 600
76. 2 x 2 − 11 x + 5 2 x squared , minus 11 x plus 5
77. x 2 − y 2 x squared , minus , y squared
78. − 1 16 s 2 + 1 negative , 1 sixteenth , s squared , plus 1
79. Error Analysis Your friend attempted to factor an expression as shown. Find the error in your friend's work. Then factor the expression correctly.

    
    Image Long Description

80. Agriculture The area in square feet of a rectangular field is x 2 − 120 x + 3500 . x squared , minus 120 x plus , 3500 , .  The width, in feet, is x − 50 . x minus 50 .  What is the length, in feet?

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

81. y 2 − y y squared , minus y
82. a b 2 − b eh , b squared , minus b
83. 10 x 2 − 90 10 x squared , minus 90
84. 3 t 2 − 24 t 3 t squared , minus 24 t
85. 2 x 2 − 74 x + 12 2 x squared , minus 74 x plus 12
86. x 2 y 2 + x y x squared , y squared , plus x y
87. What is the factored form of 4 x 2 + 15 x − 4 ? 4 x squared , plus 15 x minus 4 question mark
    1. ( 2 x + 2 ) ( 2 x − 2 ) open 2 x plus 2 close open 2 x minus 2 close
    2. ( 2 x − 4 ) ( 2 x + 1 ) open 2 x minus 4 close open 2 x plus 1 close
    3. ( 4 x + 1 ) ( x − 4 ) open 4 x plus 1 close open x minus 4 close
    4. ( 4 x − 1 ) ( x + 4 ) open 4 x minus 1 close open x plus 4 close
88. Geometry What is the volume of the shaded pipe with outer radius R, inner radius r, and height h as shown? Express your answer in completely factored form.

    

89. Open-Ended Write a quadratic trinomial that you can factor, where a ≠ 1 , a c > 0 , eh not equal to 1 comma eh c greater than 0 comma  and b < 0 . b less than 0 .  Factor the expression.
90. Writing Explain how to factor 3 x 2 + 6 x − 72 3 x squared , plus 6 x minus 72  completely.

C Challenge

Factor each expression completely.

91. 0 . 25 t 2 − 0 . 16 0 . 25 , t squared , minus 0 . 16
92. 8100 x 2 − 10 , 000 8100 , x squared . minus 10 comma 000
93. ( x + 3 ) 2 + 3 ( x + 3 ) − 54 open x plus 3 , close squared , plus 3 open x plus 3 close minus 54
94. ( x − 2 ) 2 − 15 ( x − 2 ) + 56 open x minus 2 , close squared , minus 15 open x minus 2 close plus 56
95. 6 ( x + 5 ) 2 − 5 ( x + 5 ) + 1 6 open x plus 5 , close squared , minus 5 open x plus 5 close plus 1
96. 3 ( 2 a − 3 ) 2 + 17 ( 2 a − 3 ) + 10 3 open 2 eh minus 3 , close squared , plus 17 open 2 eh minus 3 close plus 10

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