A-2 Answers to Selected Exercises 135. -4z + 4y 137. 1700 139. 150 141. 4 143. 16 145. 20 147. -1 149. -5 151. 3 153. 9 155. x and y have the same sign. 157. x and y have different signs. 159. x and y have the same sign. 161. 16; This represents the number of strokes between their scores. 163. 0.031 165. 0.026; Increased weight results in lower BAC. 167. 115.7 169. 110.9 171. 105.5 173. 122.5 175. 97.7 R.4 Exercises 1. true 3. false; 1a223 = a6 5. true 7. false; 13x22-1 = 1 3x2 9. (a) B (b) D (c) B (d) D 11. -16x7 13. n11 15. 98 17. 72m11 19. -15x5y5 21. 4m3n3 23. 210 25. -216x6 27. -16m6 29. r 24 s6 31. 256 m8 t4p8 33. -1 35. (a) B (b) C (c) B (d) C 37. - 1 64 39. - 1 625 41. 9 43. 1 16x2 45. 4 x2 47. - 1 a3 49. 16 51. x4 53. 1 r3 55. 66 57. 2r 3 3 59. 4n7 3m7 61. -4r6 63. 625 a10 65. p4 5 67. 1 2pq 69. 4 a2 71. 5 x2 73. 13 75. 2 77. - 4 3 79. This expression is not a real number. 81. (a) C (b) A (c) B (d) D 83. 4 85. 1000 87. -27 89. 256 81 91. 9 93. 4 95. y 97. k2/3 99. x3y8 101. 1 x10/3 103. 6 m1/4n3/4 105. p2 107. (a) 250 sec (b) 2-1.5 ≈0.3536 109. 1,000,000 111. 32 113. 4 115. 1 100 117. 27 R.5 Exercises 1. 5 3. binomial 5. FOIL 7. 4x4 - 28x2 9. y2 + 8y + 16 11. polynomial; degree 11; monomial 13. polynomial; degree 4; binomial 15. polynomial; degree 5; trinomial 17. polynomial; degree 11; none of these 19. not a polynomial 21. polynomial; degree 0; monomial 23. x2 - x + 2 25. 12y2 + 4 27. 6m4 - 2m3 - 7m2 - 4m 29. 28r2 + r - 2 31. 15x4 - 7x3 - 2x2 33. 12x5 + 8x4 - 20x3 + 4x2 35. -2z3 + 7z2 - 11z + 4 37. m2 + mn - 2n2 - 2km+ 5kn - 3k2 39. 16x4 - 72x2 + 81 41. x4 - 2x2 + 1 43. 4m2 - 9 45. 16x4 - 25y2 47. 16m2 + 16mn + 4n2 49. 25r2 - 30rt2 + 9t4 51. 4p2 - 12p + 9 + 4pq - 6q + q2 53. 9q2 + 30q + 25 - p2 55. 9a2 + 6ab + b2 - 6a - 2b + 1 57. y3 + 6y2 + 12y + 8 59. q4 - 8q3 + 24q2 - 32q + 16 61. p3 - 7p2 - p - 7 63. 49m2 + 28mn + 4n2 65. -14q2 + 11q - 14 67. 4p2 - 16 69. 11y3 - 18y2 + 4y 71. y - 10y2 73. -4k10/3 + 24k4/3 75. x2 - x 77. r - 2 + 1 r 79. 3y + 4 - 5 y 81. 3 + 5 m + 6 m2 83. 2x 5 + 7x4 - 5x2 + 7 85. 2 7n + 3 2m - 9 7mn 87. 2y x + 3 4 + 3w x 89. q + 8 91. t + 5 93. p - 4 + 44 p + 6 95. m2 + 2m- 1 97. x2 + 2x - 3 + -3 4x + 1 99. 4x2 + 5x + 10 + 21 x - 2 101. 2m2 + m- 2 + 6 3m + 2 103. x2 + 2 + 5x + 21 x2 + 3 105. (a) 1x + y22 (b) x2 + 2xy + y2 (c) The expressions are equivalent because they represent the same area. 107. (a) 60,501,000 ft3 (b) The shape becomes a rectangular box with a square base, with volume V = b2h. (c) If we let a = b, then V = 1 3 h1a2 + ab + b22 becomes V = 1 3 h1b2 + bb + b22, which simplifies to V = hb2. Yes, the Egyptian formula gives the same result. 109. 5.4; same 111. 2.2; 0.1 high 113. 9999 114. 3591 115. 10,404 116. 5041 R.6 Exercises 1. factoring 3. multiplying 5. sum of squares 7. (a) B (b) C (c) A 9. B 11. 121m+ 52 13. 8k1k2 + 32 15. xy11 - 5y2 17. -2p2q 412p + q2 19. 4k2m311 + 2k2 - 3m2 21. 21a + b211 + 2m2 23. 1r + 3213r - 52 25. 1m- 1212m2 - 7m+ 72 27. The completely factored form is 4xy31xy2 - 22. 29. 12s + 3213t - 52 31. 1m4 + 3212 - a2 33. 1p2 - 221q 2 + 52 35. 12a - 1213a - 42 37. 13m+ 221m+ 42 39. prime 41. 2a13a + 7212a - 32 43. 13k - 2p212k + 3p2 45. 15a + 3b21a - 2b2 47. 14x + y213x - y2 49. 2a214a - b213a + 2b2 51. 13m- 222 53. 214a + 3b22 55. 12xy + 722 57. 1a - 3b - 322 59. 13a + 4213a - 42 61. 1x2 + 421x + 221x - 22 63. 15s2 + 3t215s2 - 3t2 65. 1a + b + 421a + b - 42 67. 1p2 + 2521p + 521p - 52 69. 1x - 4 + y21x - 4 - y2 71. 1y + x - 621y - x + 62 73. 12 - a214 + 2a + a22 75. 15x - 32125x2 + 15x + 92 77. 13y3 + 5z2219y6 - 15y3z2 + 25z42 79. r1r2 + 18r + 1082 81. 13 - m- 2n219 + 3m+ 6n + m2 + 4mn + 4n22 83. 917k - 321k + 12 85. 13a - 722 87. 1a + 421a2 - a + 72 89. 91x + 1213x2 + 9x + 72 91. 1m2 - 521m2 + 22 93. 13t2 + 5214t2 - 72 95. 12b + c + 4212b + c - 42 97. 1x + y21x - 52 99. 1m- 2n21p4 + q2 101. 12z + 722 103. 110x + 7y21100x2 - 70xy + 49y22 105. 15m2 - 62125m4 + 30m2 + 362
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