59 R.5 Polynomials Find each product. Assume all variables represent positive real numbers. 71. y5/81y3/8 - 10y11/82 72. p11/513p4/5 + 9p19/52 73. -4k1k7/3 - 6k1/32 74. -5y13y9/10 + 4y3/102 75. 1x + x1/221x - x1/22 76. 12z1/2 + z21z1/2 - z2 77. 1r1/2 - r-1/222 78. 1p1/2 - p-1/221p1/2 + p-1/22 Perform each division. See Examples 7 and 8. 79. 9y2 + 12y - 15 3y 80. 80r2 - 40r + 10 10r 81. 15m3 + 25m2 + 30m 5m3 82. 64x3 - 72x2 + 12x 8x3 83. -4x7 - 14x6 + 10x4 - 14x2 -2x2 84. -8r3s - 12r2s2 + 20rs3 -4rs 85. -4m2n2 - 21mn3 + 18mn2 -14m2n3 86. -24h2k + 56hk2 - 28hk -16h2k2 87. 8wxy2 + 3wx2y + 12w2xy 4wx2y 88. 12ab2c + 10a2bc + 18abc2 6a2bc Perform each division. See Examples 9 and 10. 89. q2 + 4q - 32 q - 4 90. q2 + 2q - 35 q - 5 91. 3t2 + 17t + 10 3t + 2 92. 2k2 - 3k - 20 2k + 5 93. p2 + 2p + 20 p + 6 94. x2 + 11x + 16 x + 8 95. 3m3 + 5m2 - 5m+ 1 3m- 1 96. 8z3 - 6z2 - 5z + 3 4z + 3 97. 4x3 + 9x2 - 10x - 6 4x + 1 98. 10z3 - 26z2 + 17z - 13 5z - 3 99. 4x3 - 3x2 + 1 x - 2 100. 3x3 - 2x + 5 x - 3 101. 6m3 + 7m2 - 4m+ 2 3m+ 2 102. 10x3 + 11x2 - 2x + 3 5x + 3 103. x4 + 5x2 + 5x + 27 x2 + 3 104. k4 - 4k2 + 2k + 5 k2 + 1 (Modeling) Solve each problem. 105. Geometric Modeling Consider the figure, which is a square divided into two squares and two rectangles. (a) The length of each side of the largest square is x + y. Use the formula for the area of a square to write the area of the largest square as a power. (b) Use the formulas for the area of a square and the area of a rectangle to write the area of the largest square as a trinomial that represents the sum of the areas of the four figures that make it up. (c) Explain why the expressions in parts (a) and (b) must be equivalent. y x x y
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