0.05e: Exercises - Factoring
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A: Factor out the GCF
Exercise 0.5.A
★ Factor out the GCF.
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- Answers to odd exercises:
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1. 4x2(3x2−4x+1)
3. 4y3(5y5+7y3+10)
5. 2a2b(a2b2−3ab+4)7. x2y3(2xy2−4x2y+1)
9. (2x+3)(5x2−3)
11. (3x−1)(9x2+1)13. xn(x4n−x2n+1)
15. 2x2(x2−6x−1)
17. x2y(x2y2−3x+1)19. 7(5y+12)
21. 3x(6x2−5)
23. 4x(x2−3x+4)
25. −3x(x2−9x+4)
B: Factor 4 term Polynomials.
Exercise 0.5.B
★ Factor by grouping.
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- Answers to odd exercises:
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31. (2x+3)(x2+1)
33. (2x−1)(3x2+2)
35. (x−1)(x2−3)
37. (2x+7)(x2−5)
39. (7y+5)(2y3−1)
41. (xn+1)(x3n+2)43. (x−y)(x2+y2)
45. (x+3y)(3x2y2−1)
47. (a−4b)(ab−3)
49. (a2+b)(a2+b3)
51. (a−2b)(3x−5y)
53. xy2(x−y)(x2+y2)55. a2b2(a2+b)(a+b2)
57. (x2+1)(2x−1)
59. (x2+y2)(x−5y)
61. 2x(x−2y)(x2+y2)
63. (a+b)(x−y)
65. (x−3)(x+7)67. (m2+1)(m+1)
69. (−8x+3)(14x+3)
71. (−8x+3)(16x+3)
73. (−6x+7)(16x+7)
75. (3x−10)(3x+14)
77. (4x−3)(4x+9)
79. (5x−6)(5x+12)
C: Factor Binomials.
Exercise 0.5.C
★ I. Factor two term polynomials.
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- Answers to odd exercises:
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81. (x+8)(x−8)
83. (3+2y)(3−2y)
85. (x+9y)(x−9y)
87. (ab+2)(ab−2)
89. (ab+c)(ab−c)
91. (x2+8)(x2−8)
93. (3x+5)(x+5)
95. 3(2y−3)97. (3x+2)(x+8)
99. (x2+4)(x+2)(x−2)
101. (x2y2+1)(xy+1)(xy−1)
103. (x4+y4)(x2+y2)(x+y)(x−y)
105. (xn+yn)(xn−yn)
107. (x2n+y2n)(xn+yn)(xn−yn)
109. (x−3)(x2+3x+9)
111. (2y+3)(4y2−6y+9)113. (x−y)(x2+xy+y2)
115. (2ab+1)(4a2b2−2ab+1)
117. (xy−5)(x2y2+5xy+25)
119. (2x+3)(x2+3x+9)
121. (x+1)(7x2+5x+1)
123. (xn−yn)(x2n+xnyn+y2n)
125. (a2+4)(a4−4a2+16)127. (x+y)(x2−xy+y2)(x−y)(x2+xy+y2)
129. (xn+yn)(x2n−xnyn+y2n)(xn−yn)(x2n+xnyn+y2n)
★ II. Factor two term polynomials.
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- Answers to odd exercises:
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131. (8x+1)(8x−1)
133. (x+6y)(x−6y)
135. (ab+5)(a2b2−5ab+25)
137. (9x2+y2)(3x+y)(3x−y)
139. (x+2y)(x2−2xy+4y2)(x−2y)(x2+2xy+4y2)
141. 9x(9x−1)
143. (13m+n)(13m−n)145. (3+11y)(3−11y)
147. n(13n+1)(13n−1)
149. 6(4p2+9)
151. (2z−1)(2z+1)(4z2+1)
153. (a+3−3b)(a+3+3b)
155. (a−5)(a2+5a+25)
157. 2(m+3)(m2−3m+9)
D: Factor Trinomials, a=1.
Exercise 0.5.D
★ Factor trinomials, a=1.
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- Answers to odd exercises:
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161. (x−1)(x+6)
163. (x−2)(x+6)
165. (x−6)(x−8)
167. Prime
169. (x−9)2171. (x−5y)(x+4y)
173. (xy−5)(xy+10)
175. (a+6b)(a−12b)
177. (u−2v)(u+16v)
179. (x+y−4)(x+y+2)181. (x2−8)(x2+1)
183. (x2+4)(x2−12)
185. (y2−10)2
187. (x2+y2)(x2+2y2)
189. (a2b2−2)2191. (x3−20)(x3+2)
193. (x3+2y3)(x3−3y3)
195. (x3y3−3)(x3y3+5)
197. (xn+4)(xn+8)
199. (xn+a)2
E: Factor trinomials, a≠1
Exercise 0.5.E
★ Factor trinomials. (Leading coefficient is not one).
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- Answers to odd exercises:
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201. (3x−1)(x+7)
203. (2a+3)(3a+2)
205. (6x−5)(x+2)
207. (8y−1)(3y−4)
209. Prime
211. (2x−7)2
213. (9x+4)(3x−2)215. (6x−y)(x+4y)
217. (4ab−3)(2ab−3)
219. (2u−5v)(4u−3v)
221. (2a−3b)2
223. (x+y−1)(5x+5y−4)
225. (x2−3)(7x2−1)227. (y3−2)(4y3+5)
229. (a2b2−2)(5a2b2+9)
231. (6x3y3+5)(x3y3+2)
233. (2xn−5)(4xn+5)
235. (6xn+a)2
237. −(x−5)(3x+1)239. −(x−2)(x+12)
241. −2(x−3)(x+9)
243. 4x(x2+4x+5)
245. 2x(x+2y)(x−6y)
247. 4ab(a−3b)(a+2b)
249. 3xy(x2+5y2)2
F: Factor Trinomials.
Exercise 0.5.F
★ Factor the following trinomials.
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- Answers to odd exercises:
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251. (x−12)(x+4)
253. Prime
255. (x+5y)(x+15y)
257. −2(y−12)(y+2)
259. 2(15x−1)(5x−3)
261. (3u+v)(9u−4v)
263. (4m+9n)2265. (5x2−6)(5x2−1)
267. (x3+5y3)(x3−2y3)
269. (xn−1)2
271. (5x+3)2
273. 10(2x+9)2
275. 3u2(5u−v)2277. (m+9)(m−6)
279. (x+5y)(x+7y)
281. (a+7b)(a−3b)
283. Prime
285. 3y(y−5)(y−2)
287. (5y+9)(y+1)289. (5y+1)(2y−11)
291. −9(9a−1)(a+2)
293. (3a−1)(6a−1)
295. Prime
297. 3(x+4)(x−3)
299. 3(2a−7)(3a+1)
G: Mixed Factoring Practice.
Exercise 0.5.G
★ Mixed practice. Factor completely.
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- Answers to odd exercises:
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301. ( 2 - 5 x ) ( 2 + 5 x )
303. ( 3 x - 2 y ) ^ { 2 }
305. ( 2 a - 1 ) ( 5 a - 3 b )
307. Prime
309. 3 a b ^ { 2 } \left( 5 a ^ { 2 } + 2 a b - b ^ { 2 } \right)
311. 5 x ( 3 x + 2 ) ( 3 x - 2 )
313. - ( 10 x - 1 ) ( 2 x - 3 )
315. 3 a b ^ { 2 } ( 2 a + b ) \left( 4 a ^ { 2 } - 2 a b + b ^ { 2 } \right)
317. Prime
319. 8y(y−1)(y+3)
321. 4x(2x−3)(2x+3)323. (2x+5y)^2
325. 2xy(25x^2+36)
327. 4ab(a^2+4)(a−2)(a+2)
329. 6(x+b)(x−2c)
331. 4q(p−3)(p−1)
333. (2x−3y−5)(2x−3y+5)
335. 40a^2(2+3a)
337. (x+9)(x+4)
339. (x−8)(y+7)
341. (3s−2)^2
343. 3(x+5y)(x−5y)345. (x+5)(x^2−5x+25)
347. (3x^2−5)(2x^2−3)
349. 4x^2(6x+11)
351. (4n−7m)^2
353. 5u^2(u+3)(u−3)
355. prime
357. (b−4)(b^2+4b+16)
359. (2b+5c)(b−c)
361. 5(q+3)(q−6)
363. 10(m−5)(m+5)(m^2+25)
365. (4x -7)(4x+15)
367. (-8x +9)(16x +9)
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