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All Textbook Solutions for Elementary Algebra
In the following exercises, simplify each expression. 780. Convert 6.91105 to decimal form.In the following exercises, simplify, and write your answer in decimal form. 781. (304109)(2.2105)In the following exercises, simplify, and write your answer in decimal form. 782. 8.41034103In the following exercises, simplify, and write your answer in decimal form. 783. A helicopter flying at an altitude of 1000 feet drops a rescue package. The polynomial 16t2+1000 gives the height of the package t seconds a after it was dropped. Find the height when t=6 seconds.Find the GCF of 48 and 80.Find the GCF of 18 and 40.Find the GCF: 12x2,18x3 .Find the GCF: 12y2,24y3 .Find the GCF: 6ab4,8a2b .Find the GCF: 9m5n2,12m3n .Find the greatest common factor: 25m4,35m3,20m2 .Find the greatest common factor: 14x3,70x2,105x .Factor: 6a+24 .Factor: 2b+14 .Factor: 14x+14 .Factor: 12p+12 .Factor: 18u36 .Factor: 30y60 .Factor: 5x225x+15 .Factor: 3y212y+27 .Factor: 2x3+12x2 .Factor: 6y315y2 .Factor: 20x310x2+14x .Factor: 24y312y220y .Factor: 9xy2+6x2y2+21y3 .Factor: 3p36p2q+9pq3 .Factor: 16z64 .Factor: 9y27 .Factor: 4b2+16b .Factor: 7a2+21a .Factor: 4m(m+3)7(m+3) .Factor: 8n(n4)+5(n4) .Factor: xy+8y+3x+24 .Factor: ab+7b+8a+56 .Factor: x2+2x5x10 .Factor: y2+4y7y28 .In the following exercises, find the greatest common factor. 1. 8, 18In the following exercises, find the greatest common factor. 2. 24, 40In the following exercises, find the greatest common factor. 3. 72, 162In the following exercises, find the greatest common factor. 4. 150, 275In the following exercises, find the greatest common factor. 5. 10a, 50In the following exercises, find the greatest common factor. 6. 5b, 30In the following exercises, find the greatest common factor. 7. 3x,10x2In the following exercises, find the greatest common factor. 8. 21b2,14bIn the following exercises, find the greatest common factor. 9. 8w2,24w3In the following exercises, find the greatest common factor. 10. 30x2,18x3In the following exercises, find the greatest common factor. 11. 10p3q,12pq2In the following exercises, find the greatest common factor. 12. 8a2b3,10ab2In the following exercises, find the greatest common factor. 13. 12m2n3,30m5n3In the following exercises, find the greatest common factor. 14. 28x2y4,42x4y4In the following exercises, find the greatest common factor. 15. 10a3,12a2,14aIn the following exercises, find the greatest common factor. 16. 20y3, 28y2, 40yIn the following exercises, find the greatest common factor. 17. 35x3,10x4,5x5In the following exercises, find the greatest common factor. 18. 27p2,45p3,9p4In the following exercises, factor the greatest common factor from each polynomial. 19. 4x+20In the following exercises, factor the greatest common factor from each polynomial. 20. 8y+16In the following exercises, factor the greatest common factor from each polynomial. 21. 6m+9In the following exercises, factor the greatest common factor from each polynomial. 22. 14p+35In the following exercises, factor the greatest common factor from each polynomial. 23. 9q+9In the following exercises, factor the greatest common factor from each polynomial. 24. 7r+7In the following exercises, factor the greatest common factor from each polynomial. 25. 8m8In the following exercises, factor the greatest common factor from each polynomial. 26. 4n4In the following exercises, factor the greatest common factor from each polynomial. 27. 9n63In the following exercises, factor the greatest common factor from each polynomial. 28. 45b18In the following exercises, factor the greatest common factor from each polynomial. 29. 3x2+6x9In the following exercises, factor the greatest common factor from each polynomial. 30. 4y2+8y4In the following exercises, factor the greatest common factor from each polynomial. 31. 8p2+4p+2In the following exercises, factor the greatest common factor from each polynomial. 32. 10q2+14q+20In the following exercises, factor the greatest common factor from each polynomial. 33. 8y3+16y2In the following exercises, factor the greatest common factor from each polynomial. 34. 12x310xIn the following exercises, factor the greatest common factor from each polynomial. 35. 5x315x2+20xIn the following exercises, factor the greatest common factor from each polynomial. 36. 8m240m+16In the following exercises, factor the greatest common factor from each polynomial. 37. 12xy218x2y230y3In the following exercises, factor the greatest common factor from each polynomial. 38. 21pq2+35p2q228q3In the following exercises, factor the greatest common factor from each polynomial. 39. 2x4In the following exercises, factor the greatest common factor from each polynomial. 40. 3b+12In the following exercises, factor the greatest common factor from each polynomial. 41. 5x(x+1)+3(x+1)In the following exercises, factor the greatest common factor from each polynomial. 42. 2x(x1)+9(x1)In the following exercises, factor the greatest common factor from each polynomial. 43. 3b(b2)13(b2)In the following exercises, factor the greatest common factor from each polynomial. 44. 6m(m5)7(m5)In the following exercises, factor by grouping. 45. xy+2y+3x+6In the following exercises, factor by grouping. 46. mn+4n+6m+24In the following exercises, factor by grouping. 47. uv9u+2v18In the following exercises, factor by grouping. 48. pq10p+8q80In the following exercises, factor by grouping. 49. b2+5b4b20In the following exercises, factor by grouping. 50. m2+6m12m72In the following exercises, factor by grouping. 51. p2+4p9p36In the following exercises, factor by grouping. 52. x2+5xx15In the following exercises, factor. 53. 20x10In the following exercises, factor. 54. 5x3x2+xIn the following exercises, factor. 55. 3x27x2+6x14In the following exercises, factor. 56. x3+x2x1In the following exercises, factor. 57. x2+xy+5x+5yIn the following exercises, factor. 58. 5x33x25x3Area of a rectangle The area of a rectangle with length 6 less than the width is given by the expression w26w , where w = width. Factor the greatest common factor from the polynomial.Height of a baseball The height of a baseball t seconds after it is hit is given by the expression 16t2+80t+4 . Factor the greatest common factor from the 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: x2+6x+8 .Factor: y2+8y+15 .Factor: q2+10q+24 .Factor: t2+14t+24 .Factor: x2+19x+60 .Factor: v2+23v+60 .Factor: u29u+18 .Factor: y216y+63 .Factor: h2+4h12 .Factor: k2+k20 .Factor: x24x12 .Factor: y2y20 .Factor: r23r40 .Factor: s23s10 .Factor: m2+4m+18 .Factor: n210n+12 .Factor: 9m+m2+18 .Factor: 7n+12+n2 .Factor: u2+11uv+28v2 .Factor: x2+13xy+42y2 .Factor: a211ab+10b2 .Factor: m213mn+12n2 .Factor: x27xy10y2 .Factor: p2+15pq+20q2 .In the following exercises, factor each trinomial of the formx2+bx+c. 63. x2+4x+3In the following exercises, factor each trinomial of the formx2+bx+c. 64. y2+8y+7In the following exercises, factor each trinomial of the formx2+bx+3. 65. m2+12m+11In the following exercises, factor each trinomial of the formx2+bx+c . 66. b2+14b+13In the following exercises, factor each trinomial of the formx2+bx+c . 67. a2+9a+20In the following exercises, factor each trinomial of the formx2+bx+c . 68. m2+7m+12In the following exercises, factor each trinomial of the formx2+bx+c . 69. p2+11p+30In the following exercises, factor each trinomial of the formx2+bx+c . 70. w2+10x+21In the following exercises, factor each trinomial of the formx2+bx+c . 71. n2+19n+48In the following exercises, factor each trinomial of the formx2+bx+c . 72. b2+14b+48In the following exercises, factor each trinomial of the formx2+bx+c . 73. a2+25a+100In the following exercises, factor each trinomial of the form x2+bx+c . 74. u2+101u+100In the following exercises, factor each trinomial of the formx2+bx+c . 75. x28x+12In the following exercises, factor each trinomial of the formx2+bx+c . 76. q213q+36In the following exercises, factor each trinomial of the formx2+bx+c . 77. y218x+45In the following exercises, factor each trinomial of the formx2+bx+c . 78. m213m+30In the following exercises, factor each trinomial of the formx2+bx+c . 79. x28x+7In the following exercises, factor each trinomial of the formx2+bx+c . 80. y25y+6In the following exercises, factor each trinomial of the formx2+bx+c . 81. p2+5p6In the following exercises, factor each trinomial of the formx2+bx+c . 82. n2+6n7In the following exercises, factor each trinomial of the formx2+bx+c . 83. y26y7In the following exercises, factor each trinomial of the formx2+bx+c . 84. v22v3In the following exercises, factor each trinomial of the formx2+bx+c . 85. x2x12In the following exercises, factor each trinomial of the formx2+bx+c . 86. r22r8In the following exercises, factor each trinomial of the formx2+bx+c . 87. a23a28In the following exercises, factor each trinomial of the formx2+bx+c . 88. b213b30In the following exercises, factor each trinomial of the formx2+bx+c . 89. w25w36In the following exercises, factor each trinomial of the formx2+bx+c . 90. t23t54In the following exercises, factor each trinomial of the formx2+bx+c . 91. x2+x+5In the following exercises, factor each trinomial of the formx2+bx+c . 92. x23x9In the following exercises, factor each trinomial of the formx2+bx+c . 93. 86x+x2In the following exercises, factor each trinomial of the formx2+bx+c . 94. 7x+x2+6In the following exercises, factor each trinomial of the formx2+bx+c . 95. x21211xIn the following exercises, factor each trinomial of the formx2+bx+c . 96. 1110x+x2In the following exercises, factor each trinomial of the formx2+bxy+cy2. 97. p2+3pq+2q2In the following exercises, factor each trinomial of the formx2+bxy+cy2 . 98. m2+6mn+5n2In the following exercises, factor each trinomial of the formx2+bxy+cy2 . 99. r2+15rs+36s2In the following exercises, factor each trinomial of the formx2+bxy+cy2 . 100. u2+100uv+24v2In the following exercises, factor each trinomial of the formx2+bxy+cy2 . 101. m212mn+20n2In the following exercises, factor each trinomial of the formx2+bxy+cy2 . 102. p216pq+63q2In the following exercises, factor each trinomial of the formx2+bxy+cy2 . 103. x22xy80y2In the following exercises, factor each trinomial of the formx2+bxy+cy2 . 104. p28pq65q2In the following exercises, factor each trinomial of the formx2+bxy+cy2 . 105. m264mn65n2In the following exercises, factor each trinomial of the formx2+bxy+cy2 . 106. p22pq35q2In the following exercises, factor each trinomial of the formx2+bxy+cy2 . 107. a2+5ab24b2In the following exercises, factor each trinomial of the formx2+bxy+cy2 . 108. r2+3rs28s2In the following exercises, factor each trinomial of the formx2+bxy+cy2 . 109. x22xy14y2In the following exercises, factor each trinomial of the formx2+bxy+cy2 . 110. u28uv24v2In the following exercises, factor each trinomial of the formx2+bxy+cy2 . 111. m25mn+30n2In the following exercises, factor each trinomial of the formx2+bxy+cy2 . 112. c27cd+18d2In the following exercises, factor each expression. 113. u212u+36In the following exercises, factor each expression. 114. w2+4w32the following exercises, factor each expression. 115. x214x32In the following exercises, factor each expression. 116. y2+41y+40In the following exercises, factor each expression. 117. r220rs+64s2In the following exercises, factor each expression. 118. x216xy+64y2In the following exercises, factor each expression. 119. k2+34k+120In the following exercises, factor each expression. 120. m2+29m+120In the following exercises, factor each expression. 121. y2+10y+15In the following exercises, factor each expression. 122. z23z+28In the following exercises, factor each expression. 123. m2+mn56n2In the following exercises, factor each expression. 124. q229qr96r2the following exercises, factor each expression. 125. u217uv+30v2In the following exercises, factor each expression. 126. m231mn+30n2In the following exercises, factor each expression. 127. c28cd+26d2In the following exercises, factor each expression. 128. r2+11rs+36s2Consecutive integers Deirdre is thinking of two consecutive integers whose product is 56. The trinomial x2+x56 describes how these numbers are related. Factor the trinomial.Consecutive integers Deshawn is thinking of two consecutive integers whose product is 182. The trinomial x2+x182 describes how these numbers are related. Factor the trinomial.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.How do you determine whether to use plus or minus signs in the binomial factors of a trinomial of the form x2+bx+c where b and c may be positive or negative numbers?Will factored x2x20 as (x+5)(x4) . Bill factored it as (x+4)(x5) . Phil factored it as (x5)(x4) . Who is correct? Explain why the other two are wrong.Look at Example 7.19, where we factored y2+17y+60 . We made a table listing all pairs of factors of 60 and their sums. Do you find this kind of table helpful? Why or why not?Identify the best method to use to factor each polynomial: (a)4y2+32 (b)y2+10y+21 (c)yz+2y+3z+6Identify the best method to use to factor each polynomial: (a) ab+a+4b+4 (b) 3k2+15 (c) p2+9p+8Factor completely: 4m24m8 .Factor completely: 5k215k50 .Factor completely: 3r29r+6 .Factor completely: 2t210t+12 .Factor completely: 5x3+15x220x .Factor completely: 6y3+18y260y .Factor completely: 2a2+5a+3 .Factor completely: 4b2+5b+1 .Factor completely: 8x213x+3 .Factor completely: 10y237+7 .Factor completely: 8a23a5 .Factor completely: 6b2b15 .Factor completely: 18x23x10 .Factor completely: 30y253y21 .Factor completely: 15n285n2+100n .Factor completely: 56q3+320q296q .Factor: 6x2+13x+2 .Factor: 4y2+8y+3 .Factor: 20h2+13h15 .Factor: 6g2+19g20 .Factor: 10t2+19t15 .Factor: 3u2+8u+5 .Factor: 16x232x+12 .Factor: 18w239w+18 .In the following exercises, identify the best method to use to factor each polynomial. 135. (a) 10q2+50 (b) a25a14 (c) uv+2u+3v+6In the following exercises, identify the best method to use to factor each polynomial. 136. (a) n2+10n+24 (b) 8u2+16 (c) pq+5q+2q+10In the following exercises, identify the best method to use to factor each polynomial. 137. (a) x2+4x21 (b) ab+10b+4a+40 (c) 6c2+24In the following exercises, identify the best method to use to factor each polynomial. 138. (a) 20x2+100 (b) uv+6u+4v+24 (c) y28y+15In the following exercises, factor completely. 139. 5x2+35x+30In the following exercises, factor completely. 140. 12s2+24s+12In the following exercises, factor completely. 141. 2z22z24In the following exercises, factor completely. 142. 3u212u36In the following exercises, factor completely. 143. 7v26v+56In the following exercises, factor completely. 144. 5w230w+45In the following exercises, factor completely. 145. p38p220pIn the following exercises, factor completely. 146. q35q224qIn the following exercises, factor completely. 147. 3m321m2+30mIn the following exercises, factor completely. 148. 11n255n2+44nIn the following exercises, factor completely. 149. 5x2+10x375x2In the following exercises, factor completely. 150. 6y4+12y348y2In the following exercises, factor. 151. 2t2+7t+5In the following exercises, factor. 152. 5y2+16y+11In the following exercises, factor. 153. 11x2+34x+3In the following exercises, factor. 154. 7b2+50b+7In the following exercises, factor. 155. 4w25w+1In the following exercises, factor. 156. 5x217x+6In the following exercises, factor. 157. 6p219p+10In the following exercises, factor. 158. 21m229m+10In the following exercises, factor. 159. 4q27q2In the following exercises, factor. 160. 10y253y11In the following exercises, factor. 161. 4p2+17p15In the following exercises, factor. 162. 6u2+5u14In the following exercises, factor. 163. 16x232x+16In the following exercises, factor. 164. 81a2+153a18In the following exercises, factor. 165. 30q3+140q2+80qIn the following exercises, factor. 166. 5y3+30y235yIn the following exercises, factor. 167. 5n2+21n+4In the following exercises, factor. 168. 8w2+25w+3In the following exercises, factor. 169. 9z2+15z+4In the following exercises, factor. 170. 3m2+26m+48In the following exercises, factor. 171. 4k216k+15In the following exercises, factor. 172. 4q29q+5In the following exercises, factor. 173. 5s29s+4In the following exercises, factor. 174. 4r220r+25In the following exercises, factor. 175. 6y2+y15In the following exercises, factor. 176. 6p2+p22In the following exercises, factor. 177. 2n227n45In the following exercises, factor. 178. 12z241z11In the following exercises, factor. 179. 3x2+5x+4In the following exercises, factor. 180. 4y2+15y+6In the following exercises, factor. 181. 60y2+290y50In the following exercises, factor. 182. 6u246u16In the following exercises, factor. 183. 48z3102z245zIn the following exercises, factor. 184. 90n3+42n2216nIn the following exercises, factor. 185. 16s2+40s+24In the following exercises, factor. 186. 24p2+160p+96In the following exercises, factor. 187. 48y2+12y36In the following exercises, factor. 188. 30x2+105x60In the following exercises, factor. 189. 12y229y+14In the following exercises, factor. 190. 12x2+36y24zIn the following exercises, factor. 191. a2a20In the following exercises, factor. 192. m2m12In the following exercises, factor. 193. 6n2+5n4In the following exercises, factor. 194. 12y237y+21In the following exercises, factor. 195. 2p2+4p+3In the following exercises, factor. 196. 3q2+6q+2In the following exercises, factor. 197. 13z2+39z26In the following exercises, factor. 198. 5r2+25r+30In the following exercises, factor. 199. x2+3x28In the following exercises, factor. 200. 6u2+7u5In the following exercises, factor. 201. 3p2+21pIn the following exercises, factor. 202. 7x221xIn the following exercises, factor. 203. 6r2+30r+36In the following exercises, factor. 204. 18m2+15m+3In the following exercises, factor. 205. 24n2+20n+4In the following exercises, factor. 206. 4a2+5a+2In the following exercises, factor. 207. x2+2x24In the following exercises, factor. 208. 2b27b+4Height of a toy rocket The height of a toy rocket launched with an initial speed of 80 feet per second from the balcony of an apartment building is related to the number of seconds, t, since it is launched by the trinomial 16t2+80t+96 . Completely factor the trinomial.Height of a beach ball The height of a beach ball tossed up with an initial speed of 12 feet per second from a height of 4 feet is related to the number of seconds, t, since it is tossed by the trinomial 16t2+12t+4 . Completely factor the trinomial.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?What are the questions, in order, that you ask yourself as you start to factor a polynomial? What do you need to do as a result of the answer to each question?On your paper draw the chart that summarizes the factoring strategy. Try to do it without looking at the book. When you are done, look back at the book to finish it or verify it.