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All Textbook Solutions for Intermediate Algebra

In the following exercises, factor by grouping. 43. u2u+6u6 In the following exercises, factor by grouping. 44. x2x+4x4 In the following exercises, factor by grouping. 45. 9p23p20 In the following exercises, factor by grouping. 46. 16q28q35 In the following exercises, factor by grouping. 47. mn6m4n+24 In the following exercises, factor by grouping. 48. r23rr+3 In the following exercises, factor by grouping. 49. 2x214x5x+35 In the following exercises, factor by grouping. 50. 4x236x3x+27 In the following exercises, factor. 51. 18xy227x2y In the following exercises, factor. 52. 4x3y5x2y3+12xy4 In the following exercises, factor. 53. 3x37x2+6x14 In the following exercises, factor. 54. x3+x2x1 In the following exercises, factor. 55. x2+xy+5x+5y In the following exercises, factor. 56. 5x33x2+5x3 What does it mean to say a polynomial is in factored form?How do you check result after factoring a polynomial?The greatest common factor of 36 and 60 is 12. Explain what this means.What is the GCF of y4, y5, and y10? Write a general rule that tells you how to find the GCF of ya, yb, and yc.Factor: q2+10q+24 .Factor: t2+14t+24 .Factor: u29u+18 .Factor: y216y+63 .Factor: 9m+m2+18 .Factor: 7n+12+n2 .Factor: a211ab+10b2 .Factor: m213mn+12n2 .Factor: x27xy10y2 .Factor: p2+15pq+20q2 .Factor completely: 5x3+15x220x .Factor completely: 6y3+18y260y .Factor completely using trial and error: 2a2+5a+3 .Factor completely using trial and error: 4b2+5b+1 .Factor completely using trial and error: 8x213x+3 .Factor completely using trial and error: 10y237y+7 .Factor completely using trial and error: 18x23xy10y2 .Factor completely using trial and error: 30x253xy21y2 .Factor completely using trial and error: 15n385n2+100n .Factor completely using trial and error: 56q3+320q296q .Factor using the ‘ac’ method: 6x2+13x+2 .Factor using the ‘ac’ method: 4y2+8y+3 .Factor using the ‘ac’ method: 16x232x+12 .Factor using the ‘ac’ method: 18w239w+18 .Factor by substitution: h4+4h212 .Factor by substitution: y4y220 .Factor by substitution: (x5)2+6(x5)+8 .Factor by substitution: (y4)2+8(y4)+15 .In the following exercises, factor each trinomial of the form x2+bx+c. 61. p2+11p+30 In the following exercises, factor each trinomial of the form x2+bx+c. 62. w2+10x+21 In the following exercises, factor each trinomial of the form x2+bx+c. 63. n2+19n+48 In the following exercises, factor each trinomial of the form x2+bx+c. 64. b2+14b+48 In the following exercises, factor each trinomial of the form x2+bx+c. 65. a2+25a+100 In the following exercises, factor each trinomial of the form x2+bx+c. 66. u2+101u+100 In the following exercises, factor each trinomial of the form x2+bx+c. 67. x28x+12 In the following exercises, factor each trinomial of the form x2+bx+c. 68. q213q+36 In the following exercises, factor each trinomial of the form x2+bx+c. 69. y218x+45 In the following exercises, factor each trinomial of the form x2+bx+c. 70. m213m+30 In the following exercises, factor each trinomial of the form x2+bx+c. 71. x28x+7 In the following exercises, factor each trinomial of the form x2+bx+c. 72. y25y+6 In the following exercises, factor each trinomial of the form x2+bx+c. 73. 5p6+p2 In the following exercises, factor each trinomial of the form x2+bx+c. 74. 6n7+n2 In the following exercises, factor each trinomial of the form x2+bx+c. 75. 86x+x2 In the following exercises, factor each trinomial of the form x2+bx+c. 76. 7x+x2+6 In the following exercises, factor each trinomial of the form x2+bx+c. 77. x21211x In the following exercises, factor each trinomial of the form x2+bx+c. 78. 1110x+x2 In the following exercises, factor each trinomial of the form x2+bxy+cy2. 79. x22xy80y2 In the following exercises, factor each trinomial of the form x2+bxy+cy2. 80. p28pq65q2 In the following exercises, factor each trinomial of the form x2+bxy+cy2. 81. m264mn65n2 In the following exercises, factor each trinomial of the form x2+bxy+cy2. 82. p22pq35q2 In the following exercises, factor each trinomial of the form x2+bxy+cy2. 83. a2+5ab24b2 In the following exercises, factor each trinomial of the form x2+bxy+cy2. 84. r2+3rs28s2 In the following exercises, factor each trinomial of the form x2+bxy+cy2. 85. x23xy14y2 In the following exercises, factor each trinomial of the form x2+bxy+cy2. 86. u28uv24v2 In the following exercises, factor each trinomial of the form x2+bxy+cy2. 87. m25mn+30n2 In the following exercises, factor each trinomial of the form x2+bxy+cy2. 88. c27cd+18d2 In the following exercises, factor completely using trial and error. 89. p38p220p In the following exercises, factor completely using trial and error. 90. q35q224q In the following exercises, factor completely using trial and error. 91. 3m321m2+30m In the following exercises, factor completely using trial and error. 92. 11n355n2+44n In the following exercises, factor completely using trial and error. 93. 5x4+10x375x2 In the following exercises, factor completely using trial and error. 94. 6y4+12y348y2 In the following exercises, factor completely using trial and error. 95. 2t2+7t+5 In the following exercises, factor completely using trial and error. 96. 5y2+16y+11 In the following exercises, factor completely using trial and error. 97. 11x2+34x+3 In the following exercises, factor completely using trial and error. 98. 7b2+50b+7 In the following exercises, factor completely using trial and error. 99. 4w25w+1 In the following exercises, factor completely using trial and error. 100. 5x217x+6 In the following exercises, factor completely using trial and error. 101. 4q27q2 In the following exercises, factor completely using trial and error. 102. 10y253y11 In the following exercises, factor completely using trial and error. 103. 6p219pq+10q2 In the following exercises, factor completely using trial and error. 104. 21m229mn+10n2 In the following exercises, factor completely using trial and error. 105. 4a2+17ab15b2 In the following exercises, factor completely using trial and error. 106. 6u2+5uv14v2 In the following exercises, factor completely using trial and error. 107. 16x232x16 In the following exercises, factor completely using trial and error. 108. 81a2+153a+18 In the following exercises, factor completely using trial and error. 109. 30q3140q280q In the following exercises, factor completely using trial and error. 110. 5y330y2+35y In the following exercises, factor using the ‘ac’ method. 111. 5n2+21n+4 In the following exercises, factor using the ‘ac’ method. 112. 8w2+25w+3 In the following exercises, factor using the ‘ac’ method. 113. 4k216k+15 In the following exercises, factor using the ‘ac’ method. 114. 5s29s+4 In the following exercises, factor using the ‘ac’ method. 115. 6y2+y15 In the following exercises, factor using the ‘ac’ method. 116. 6p2+p22 In the following exercises, factor using the ‘ac’ method. 117. 2n227n45 In the following exercises, factor using the ‘ac’ method. 118. 12z241z11 In the following exercises, factor using the ‘ac’ method. 119. 60y2+290y50 In the following exercises, factor using the ‘ac’ method. 120. 6u246u16 In the following exercises, factor using the ‘ac’ method. 121. 48z3102z245z In the following exercises, factor using the ‘ac’ method. 122. 90n3+42n2216n In the following exercises, factor using the ‘ac’ method. 123. 16s2+40s+24 In the following exercises, factor using the ‘ac’ method. 124. 24p2+160p+96 In the following exercises, factor using the ‘ac’ method. 125. 48y2+12y36 In the following exercises, factor using the ‘ac’ method. 126. 30x2+105x60 In the following exercises, factor using substitution. 127. x4x212 In the following exercises, factor using substitution. 128. x4+2x28 In the following exercises, factor using substitution. 129. x43x228 In the following exercises, factor using substitution. 130. x413x230 In the following exercises, factor using substitution. 131. (x3)25(x3)36 In the following exercises, factor using substitution. 132. (x2)23(x2)54 In the following exercises, factor using substitution. 133. (3y2)2(3y2)2 In the following exercises, factor using substitution. 134. (5y1)23(5y1)18 In the following exercises, factor each expression using any method. 135. u212u+36 In the following exercises, factor each expression using any method. 136. x214x32 In the following exercises, factor each expression using any method. 137. r220rs+64s2 In the following exercises, factor each expression using any method. 138. q229qr96r2 In the following exercises, factor each expression using any method. 139. 12y229y+14 In the following exercises, factor each expression using any method. 140. 12x2+36y24z In the following exercises, factor each expression using any method. 141. 6n2+5n4 In the following exercises, factor each expression using any method. 142. 3q2+6q+2 In the following exercises, factor each expression using any method. 143. 13z2+39z26 In the following exercises, factor each expression using any method. 144. 5r2+25r+30 In the following exercises, factor each expression using any method. 145. 3p2+21p In the following exercises, factor each expression using any method. 146. 7x221x In the following exercises, factor each expression using any method. 147. 6r2+30r+36 In the following exercises, factor each expression using any method. 148. 18m2+15m+3 In the following exercises, factor each expression using any method. 149. 24n2+20n+4 In the following exercises, factor each expression using any method. 150. 4a2+5a+2 In the following exercises, factor each expression using any method. 151. x44x212 In the following exercises, factor each expression using any method. 152. x47x28 In the following exercises, factor each expression using any method. 153. (x+3)29(x+3)36 In the following exercises, factor each expression using any method. 154. (x+2)225(x+2)54 Many trinomials of the form x2+bx+c factor into the product of two binomials (x+m)(x+n) . Explain how you find the values of m and n.Tommy factored x2x20 as (x+5)(x4) . Sara factored it as (x+4)(x5) . Ernesto factored it as (x5)(x4) . Who is correct? Explain why the other two are wrong.List, in order, all the steps you take when using the “ac” method to factor a trinomial of the form ax2+bx+c .How is the “ac” method similar to the “undo FOIL” method? How is it different?Factor: 4x2+12x+9 .Factor: 9y2+24y+16 .Factor: 64y280y+25 .Factor: 16z272z+81 .Factor: 49x2+84xy+36y2 .Factor: 64m2+112mn+49n2 .Factor: 8x2y24xy+18y .Factor: 27p2q+90pq+75q .Factor: 121m21 .Factor: 81y21 .Factor: 196m225n2 .Factor: 121p29q2 .Factor: 2x4y232y2 .Factor: 7a4c27b4c2 .Factor: x210x+25y2 .Factor: x2+6x+94y2 .Factor: x3+27 .Factor: y3+8 .Factor: 8x327y3 .Factor: 1000m3125n3 .Factor: 500p3+4q3 .Factor: 432c3+686d3 .Factor: (y+1)327y3 .Factor: (n+3)3125n3 .In the following exercises, factor completely using the perfect square trinomials pattern. 159. 16y2+24y+9 In the following exercises, factor completely using the perfect square trinomials pattern. 160. 25v2+20v+4 In the following exercises, factor completely using the perfect square trinomials pattern. 161. 36s2+84s+49 In the following exercises, factor completely using the perfect square trinomials pattern. 162. 49s2+154s+121 In the following exercises, factor completely using the perfect square trinomials pattern. 163. 100x220x+1 In the following exercises, factor completely using the perfect square trinomials pattern. 164. 64z216z+1 In the following exercises, factor completely using the perfect square trinomials pattern. 165. 25n2120n+144 In the following exercises, factor completely using the perfect square trinomials pattern. 166. 4p252p+169 In the following exercises, factor completely using the perfect square trinomials pattern. 167. 49x2+28xy+4y2 In the following exercises, factor completely using the perfect square trinomials pattern. 168. 25r2+60rs+36s2 In the following exercises, factor completely using the perfect square trinomials pattern. 169. 100y252y+1 In the following exercises, factor completely using the perfect square trinomials pattern. 170. 64m234m+1 In the following exercises, factor completely using the perfect square trinomials pattern. 171. 10jk2+80jk+160j In the following exercises, factor completely using the perfect square trinomials pattern. 172. 64x2y96xy+36y In the following exercises, factor completely using the perfect square trinomials pattern. 173. 75u430u3v+3u2v2 In the following exercises, factor completely using the perfect square trinomials pattern. 174. 90p4+300p4q+250p2q2 In the following exercises, factor completely using the difference of squares pattern, if possible. 175. 25v21 In the following exercises, factor completely using the difference of squares pattern, if possible. 176. 169q21 In the following exercises, factor completely using the difference of squares pattern, if possible. 177. 449x2 In the following exercises, factor completely using the difference of squares pattern, if possible. 178. 12125s2 In the following exercises, factor completely using the difference of squares pattern, if possible. 179. 6p2q254p2 In the following exercises, factor completely using the difference of squares pattern, if possible. 180. 98r372r In the following exercises, factor completely using the difference of squares pattern, if possible. 181. 24p2+54 In the following exercises, factor completely using the difference of squares pattern, if possible. 182. 20b2+140 In the following exercises, factor completely using the difference of squares pattern, if possible. 183. 121x2144y2 In the following exercises, factor completely using the difference of squares pattern, if possible. 184. 49x281y2 In the following exercises, factor completely using the difference of squares pattern, if possible. 185. 169c236d2 In the following exercises, factor completely using the difference of squares pattern, if possible. 186. 36p249q2 In the following exercises, factor completely using the difference of squares pattern, if possible. 187. 16z41 In the following exercises, factor completely using the difference of squares pattern, if possible. 188. m4n4 In the following exercises, factor completely using the difference of squares pattern, if possible. 189. 162a4b232b2 In the following exercises, factor completely using the difference of squares pattern, if possible. 190. 48m4n2243n2 In the following exercises, factor completely using the difference of squares pattern, if possible. 191. x216x+64y2 In the following exercises, factor completely using the difference of squares pattern, if possible. 192. p2+14p+49q2 In the following exercises, factor completely using the difference of squares pattern, if possible. 193. a2+6a+99b2 In the following exercises, factor completely using the difference of squares pattern, if possible. 194. m26m+916n2 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 195. x3+125 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 196. n6+512 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 197. z627 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 198. v3216 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 199. 8343t3 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 200. 12527w3 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 201. 8y3125z3 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 202. 27x364y3 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 203. 216a3+125b3 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 204. 27y3+8z3 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 205. 7k3+56 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 206. 6x348y3 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 207. 2x216x2y3 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 208. 2x3y216y5 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 209. (x+3)3+8x3 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 210. (x+4)327x3 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 211. (y5)364y3 In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 212. (y5)3+125y3 In the following exercises, factor completely. 213. 64a225 In the following exercises, factor completely. 214. 121x2144 In the following exercises, factor completely. 215. 27q23 In the following exercises, factor completely. 216. 4p2100 In the following exercises, factor completely. 217. 16x272x+81 In the following exercises, factor completely. 218. 36y2+12y+1 In the following exercises, factor completely. 219. 8p2+2 In the following exercises, factor completely. 220. 81x2+169 In the following exercises, factor completely. 221. 1258y3 In the following exercises, factor completely. 222. 27u3+1000 In the following exercises, factor completely. 223. 45n2+60n+20 In the following exercises, factor completely. 224. 48q324q2+3q In the following exercises, factor completely. 225. x210x+25y2 In the following exercises, factor completely. 226. x2+12x+36y2 In the following exercises, factor completely. 227. (x+1)3+8x3 In the following exercises, factor completely. 228. (y3)364y3 Why was it important to practice using the binomial squares pattern in the chapter on multiplying polynomials?How do you recognize the binomial squares pattern?Explain why n2+25(n+5)2 . Use algebra, words, or pictures.Maribel factored y230y+81 as (y9)2 . Was she right or wrong? How do you know?Factor completely: 8y3+16y224y .Factor completely: 5y315y2270y .Factor completely: 16x336x .Factor completely: 27y248 .Factor completely: 4x2+20xy+25y2 .Factor completely: 9x224xy+16y2 .Factor completely: 50x3y+72xy .Factor completely: 27xy3+48xy .Factor completely: 250m3+432n3 .Factor completely: 2p3+54q3 .Factor completely: 4a5b64ab .Factor completely: 7xy57xy .Factor completely: 6x212xc+6bx12bc .Factor completely: 16x2+24xy4x6y .Factor completely: 4p2q16pq+12q .Factor completely: 6pq29pq6p .Factor completely: 4x212xy+9y225 .Factor completely: 16x224xy+9y264 .In the following exercises, factor completely. 233. 2n2+13n7 In the following exercises, factor completely. 234. 8x29x3 In the following exercises, factor completely. 235. a5+9a3 In the following exercises, factor completely. 236. 75m3+12m In the following exercises, factor completely. 237. 121r2s2 In the following exercises, factor completely. 238. 49b236a2 In the following exercises, factor completely. 239. 8m232 In the following exercises, factor completely. 240. 36q2100 In the following exercises, factor completely. 241. 25w260w+36 In the following exercises, factor completely. 242. 49b2112b+64 In the following exercises, factor completely. 243. m2+14mn+49n2 In the following exercises, factor completely. 244. 64x2+16xy+y2 In the following exercises, factor completely. 245. 7b2+7b42 In the following exercises, factor completely. 246. 30n2+30n+72 In the following exercises, factor completely. 247. 3x4y81xy In the following exercises, factor completely. 248. 4x5y32x2y In the following exercises, factor completely. 249. k416 In the following exercises, factor completely. 250. m481 In the following exercises, factor completely. 251. 5x5y280xy2 In the following exercises, factor completely. 252. 48x5y2243xy2 In the following exercises, factor completely. 253. 15pq15p+12q12 In the following exercises, factor completely. 254. 12ab6a+10b5 In the following exercises, factor completely. 255. 4x2+40x+84 In the following exercises, factor completely. 256. 5q215q90 In the following exercises, factor completely. 257. 4u5+4u2v3 In the following exercises, factor completely. 258. 5m4n+320mn4 In the following exercises, factor completely. 259. 4c2+20cd+81d2 In the following exercises, factor completely. 260. 25x2+35xy+49y2 In the following exercises, factor completely. 261. 10m46250 In the following exercises, factor completely. 262. 3v4768 In the following exercises, factor completely. 263. 36x2y+15xy6y In the following exercises, factor completely. 264. 60x2y75xy+30y In the following exercises, factor completely. 265. 8x327y3 In the following exercises, factor completely. 266. 64x3+125y3 In the following exercises, factor completely. 267. y61 In the following exercises, factor completely. 268. y6+1 In the following exercises, factor completely. 269. 9x26xy+y249 In the following exercises, factor completely. 270. 16x224xy+9y264 In the following exercises, factor completely. 271. (3x+1)26(3x+1)+9 In the following exercises, factor completely. 272. (4x5)27(4x5)+12

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