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Solving EquationsClasswork

Solve the following equations. Show all work.

1. 3x – 4x + 6 = -2x + 7 2. 5m + 2m – 8 = 4m – 5

3. -6(n + 3) – 4 = -2(n – 3) – 4 4. 2(p + 4) – 8 = -2(p + 9) – 5

5. 5x – 3 – 2x – 8 = 3x – 4 + 2 6. 8y – 10 + 4 = 6y – 2y – 5

7. 4 – (x – 8) = 3 + 2x 8. 3 – 2(m + 4) = 5 – 6m

9. 4p + 3(p + 1) = 2(2p – 6) 10. 7(x – 9) – 20 = -6(x + 3)

Alg. II – Fund. Skills ~1~ NJCTL.org

Solving EquationsHomework


11. 2x – 8x – 4 + 3 = -5x + 4 12. 3(m – 9) + 2(m + 3) = -6

13. 4x + 5 – 8x + 10 = 2x – 12 14. 4(x + 6) – 10 = 2(2x – 3)

15. 5p + 12 – 8 + 2p = 6(p + 4) – 2 16. 2(m + 3) – 4 = 5(m + 1) – 6

17. 6(k – 3) – (k – 4) = -(k + 6) – 1 18. 5(2n – 5) – 3 = 2(3n – 4) – 8

19. 4(x – 12) – 6x = 2x – 10 20. 3y – 10 – 11y – 6 = -4y – 13

Spiral Review21. Work out: 22. Add: 23. Multiply: 24. Evaluate, use p = 4, q = 5:

10 × 24 ÷ 3 × 12 2 23+1 14

316∙ 425∙ 1524 6 + (3p ÷ 4) + 2q


Equations with FractionsClasswork


25. x2+ 32=45 26.

m3

+ 2m4

=3m4

+2

27. 2 y5

+ 56=3 y2

+ 25

28. k3+7= k

5−4

29. 3m2

+ 47=2m3

−1 30. 25k−32k=4

31. 35x+ 14−23x=53

32. p2+6= p

4−73

33. 9m2

−6=3m2

+4 34. 6 x5

−3 x2

=6


Equations with FractionsHomework


35. x4+ 23= x3+ 14 36. 23m−4

5=15m−2

37. 3k2

+ 15= k5−23

38. n4+1=2n

5+6

39. 6 y5

−2 y3

=7 40. 34x−85=25x−32

41. 67x+ 23=13x−87

42. 65y+ 27y−1=2

43. 5 p2

+3=2 p3

−4 44. 9m4

−5m2

=5m3


Spiral Review45. Subtract: 46. Divide: 47. Work out: 48. Evaluate, use p = - 6, q = - 3

53−25

516÷4 [(-17) – (8-1)] ÷ (-4) p(q ÷ 3 – p)

FormulasClasswork

Solve the following formulas for the specified variable:

49. a2 + b2 = c2 for b2 50. 2mp−3 l=4 for p

51. 3kl+2m=5m+3 for k 52. 5p + 6n = -4p – 5 for p

53. kn−3=ln−4 for n 54. mkl3

=A for k

55. 6x – 3y = 4xy + 2 for x 56. 8mn – m = 5 for m

57. 10mn2

6=k form 58. 6k + 2 – m = 3k + 4 for k


FormulasHomework

Solve the following formulas for the specified variable:

59. 3(k + 4) = 5m + 1 for k 60. 2 l+2w=P for l

61. 5mn3

=M for n 62. 6kp+lp=5 for p

63. 7mn – 8 = 8mk + 2 for m 64. 15mnl2

=6 form

65. 6 ln−4k=4 lm−4 for l 66. 10k + p = a + bp for p

67. 6abp – 2p = 7 for p 68. 8mnk

=16 for k


Spiral Review69. Work out: 70. Add: 71. Multiply: 72. Evaluate, use k = 6

[(-28) × 2) ÷ ((-8) – (-1)] 23+3 45 2 23

∙3 45 1 + 4(2 – 3k)

Solving InequalitiesClasswork

Solve the following Inequalities. Show all work.

73. 3x – 4 ≥ -2x + 6 74. 2m – 7< 5m – 9

75. 3(m – 4) ≤ -8(m + 2) – 4 76. –(3m – 1) – 5 > -2(m + 3)

77. -4(x + 6) – 9 > 2(x – 9) 78. 4y – 3 – 6y ≤ 3y – 10 – 4

79. 8 – (p + 3) < -4(p – 6) 80. 6 – 2k – 9 ≥ 3k – 2k – 1


81. 9b + 2 – 8b > 4b + 12 82. 6(2m – 3) – 4 ≤ 6m – 4

Solving InequalitiesHomework

Solve the following Inequalities. Show all work.

83. 2x – 12 < 8x + 7 84. 3(x – 3) + 2 ≥ 4(x – 5)

85. -2(x – 8) > -4(x + 3) 86. 5x – 3x + 7 ≤ x – 9 – 2

87. 7p + 3 – 5p ≥ 2p + 6 – 5p 88. -3(m – 4) – (m – 3) < m + 1

89. -6m – 9 – 4 < 2m + 3 – 9 90. 5(k – 3) – 2(k + 4) ≥ 2k + 7

91. 3(2m – 5) + 7 ≤ 4(2m – 3) + 4 92. 10m – 7 – 3m – 5 > 6m – 3m + 2


Spiral Review93. Workout: 94. Add: 95. Divide: 96. Evaluate, use x = 5

(-26 + 8) ÷ (-6 + 4) 2 27+3 57 1 23

÷2 14 -2(-6x – 9) + 4

Factoring out the GCFClasswork

Factor out the GCF from the following:

97. 6a3b + 3ab2 98. 4am3 + 8am2 – 4am 99. 3xy6 + 2xy4 – 6xy2

100. 6x3y2 – 3x2y 101. 10p3q – 15p3q2 – 5p2q2 102. 8m4n3 + 12m4n2 – 2m3n3

103. -12a3b4 + 4a2b4 + 10ab4 104. 7m3n3 – 7m3n2 + 14m3 105. -6x3y2 + 3x3y + 6x3

106. 6m3n2 – 12m4n2

Factoring out the GCFHomework

Factor out the GCF from the following:

107. 8x3y – 4x2y2 108. 8m3n3 – 4m2n3 – 32mn3 109. -18p3q2 + 3pq

110. -8xy – 16x + 8x2 111. 2p6 + 3p4 + p 112. 12m5n2 + 9m4n3 + 3m3n4

113. -6p4 + 9p3q – 3p3 114. 2xy4 – 6x3y4 + 12x4y4 115. –x3y + x2 + 3x


116. 12m3n – 2mn2 – 2mn 117. a8b + a6b2 + a3b4

Spiral Review118. Multiply: 119. Divide: 120. Work out: 121. Evaluate, use v = 2

3 14∙ 53 3

12÷ 23 (-9) – (-1) - 22 7(1 + 10v) – 8(-6v – 3)

Factoring x 2 + bx + c Classwork

Factor the following:

122. x2 – 5x – 24 123. a2 – 5ab + 6b2 124. y2 + 10y + 25

125. m2 – mn – 6n2 126. x2 – 2xy + y2 127. a2 + ab – 12b2

128. p2 + 10p + 24 129. x2 – 6xy + 8y2 130. p2 – 13p + 30

131. a2 + 7ab + 12b2

Factoring x 2 + bx + c Homework


132. m2 – 2m – 24 133. a2 – 13a + 12 134. n2 + n – 6

135. x2 – 10xy + 21y2 136. x2 + 11xy + 18y2 137. m2 – 4m – 5

138. a2 + 6ab – 16b2 139. x2 – 12x + 20 140. n2 + 7n + 12


141. a2 – 6ab – 27b2

Spiral Review142. Work out: 143. Multiply: 144. Divide 145. Evaluate, use x = 5:

5 – 4 [(-2) – (-2)] 2 34∙ 4 23 2 34

÷ 4 23 -2(-6x – 9) + 4

Factoring ax 2 + bx + c Classwork

146. 2x2 + 7x + 3 147. 6x2 – x – 2 148. 5a2 + 17a – 12

149. 6m2 - 5mn + n2 150. 6p2 + 37p + 6 151. 12b2 + bc – 6c2

152. 4m2 + 17m + 15 153. 4c2 + 20cd + 25d2 154. 12m2 – 20m + 3

155. 24m2 – 50mp + 25p2

Factoring ax 2 + bx + c Homework

156. 6x2 – 5x + 1 157. 15p2 – 22p – 5 158. 10m2 + 13m – 3

159. 12x2 – 7xy + y2 160. 4p2 + 24p + 35 161. 15m2 – 13mn + 2n2

162. 2p2 + 13p + 15 163. 4x2 + 5xy + y2 164. 6p2 – 25p + 25


165. 20m2 – 9mn + n2

Spiral Review166. Work out: 167. Subtract: 168. Evaluate, use k = 6

(52 – 1) × 4 + 33 – (4 + 8) 4 13−2 5

6 1 – 4(2 – 3k) + 3k2 – 2k – 4

Factoring a 2 – b 2 , a 3 – b 3 , a 3 + b 3 Classwork


169. a3 – 1 170. 25x2 – 16y2 171. 121a2 – 16b2

172. 27x3 + 8y3 173. a3b3 – c3 174. 4x2y2 – 1

175. 36m2 – 25n2 176. 8m3 + n3 177. a2 – 49

178. 4x2 + 25

Factoring a 2 – b 2 , a 3 – b 3 , a 3 + b 3 Homework


179. y3 + 27 180. 64m3 – 1 181. p2 – 36q2

182. m2n2 – 4 183. x2 + 16 184. 8x3 – 27y3


185. p3 – q3r3 186. 125m3 – 1 187. 25x2 – 81

188. 100x2 – y2

Spiral Review189. Work out: 190. Simplify: 191. Work out: 192. Evaluate, use x = 1, z = 610 × [(-10) + 1] ÷ (-9) 3 – 5 [(-3) – (-1)] (-3) – (-6) - 52 z ÷ 6 + x + x – 5

Factoring by GroupingClasswork

Factor the following by grouping:

193. 2xy + 5x + 8y + 20 194. 9mn – 3m – 15n + 5

195. 2xy – 10x – 3y + 15 196. 10rs – 25r + 6s – 15

197. 10pq – 2p – 5q + 1 198. 10mn + 5m + 6n + 3

199. xy – x + zy – z 200. 2km + 14k – 9m – 63

201. zx – zy + 4x – 4y 202. 6x + 15 – 8xy – 20y

Factoring by GroupingHomework

Factor the following by grouping:

203. 6mp – 2m – 15p + 5 204. 6xy + 15x + 4y + 10

205. 4rs – 4r + 3s – 3 206. 6tr – 9t – 2r + 3

207. 8mn + 4m + 6n + 3 208. 3xy – 4x – 15y + 20


209. mn – m – n + 1 210. 6qr + 15q – 8r – 20

211. 10mn – 15m – 6n + 9 212. 9pq – 12p – 12q + 16

Spiral Review213. Add: 214. Subtract: 215. Multiply: 216. Divide:

3 23+5 15 5

56−2 23

1225∙ 1524∙ 1635 3

45÷2 16

Factoring CompletelyClasswork

Factor each of the following as much as possible.

217. 3x3 – 12x2 + 36x 218. 6m3 + 4m2 – 2m 219. 3a3b – 48ab

220. 54x4 + 2xy3 221. x4y + 12x3y + 20x2y 222. -6m3n – 21m2n + 12mn

223. 4p2q2 – 12p2q – 16pq2 + 48pq 224. -16x6 – 2x3y3 225. -10m4n + 35m3n – 15m2n

226. 100p3 – 64pq2

Factoring CompletelyHomework

Factor each of the following as much as possible.

227. 3m3 – 3mn2 228. -6x3 – 28x2 + 10x 229. 18a3b – 50ab

230. x4y + 27xy 231. -12r3 – 21r2 – 9r 232. 2x2y2 – 2x2y – 2xy2 + 2xy


233. 6m3n – 5m2n2 + mn2 234. –p3q + pq3 235. 60x2 + 230x + 200

236. -8m3n – 12m2n – 4mn

Spiral Review237. Work out: 238. Simplify: 239. Add: 240. Evaluate, use x = -3, y = 2

8(-4) (2)(-1) + (4)2 172 - (12 - 4)2 + 2 227+5 35 -3x + 2y – xy + x

Solving by FactoringClasswork

Solve the following equations by factoring:

241. x3 – 16x = 0 242. 2x2 + x – 3 = 0 243. m3 + 11m2 + 30m = 0

244. 4r2 = -8r + 5 245. x2 + 42 = 13x 246. 12p2 + 9p = -3p3

247. 2r3 = 14r + 3r2 248. 4y3 + 4y2 = 80y 249. 5x = 3x3 + 14x2

250. m3 + 2m2 = 3m

Solving by FactoringHomework

Solve the following equations by factoring:

251. 2x3 – 20x2 + 48x = 0 252. 3m3 + 36m2 + 96n = 0 253. 2p3 = 128p


254. 6m3 + 5m2 = 4m 255. 3k3 + 3k = 10k2 256. 16p3 = 4p

257. 6r2 + 5 = 17r 258. 2x2 + 24 = 19x 259. 4x3 – 9x = 0

260. 6k3 = 21k2 + 90k

Spiral Review261. Work out: 262. Solve: 263. Factor: 264. Solve:4 – 5(2 + 3(4)) 2x + 3x – 7 = x + 5 25x2 – 36 4(x – 5) – (3x + 3) > 4x + 2

Multiplying Powers of the Same BaseClasswork

Simplify the following:

265. (x2y5)(x4y) 266. (-2m3n4)(4mn4) 267. (7x2y)(-3x5y4)

268. (4pq)(3p3q5) 269. (-3mnp)(-5mnp3) 270. (10k4r3)(2kr6)

271. –(3x2yz4)(2x4z)(4x3y2z5) 272. (3p2q6)(4p2q5) 273. (-5r3s4)(3r5s2)

274. (2xy5)(-5xy3)

Multipling Powers of the Same BaseHomework


275. (4x3y5)(-3x2y) 276. (-m4n4)(6mn3) 277. (12r3s5)(3r7s2)

278. (-5x2y6z3)(2xy9z2) 279. (4r2s5)(5r2s8) 280. -(m3n8p3)(m2np)


281. (4pqr)(3pq3r5) 282. (-2mn3)(-4m3n2) 283. (4x2y4)(7x2y)

284. (-6m3n9)(2m4n8)(-m3n2) 285. (-4x4y5)(3xy4)

Spiral Review286. Solve: 287. Add: 288. Solve: 289. Evaluate, use x = -4, y = 3

2(x + 4) – 3(x – 3) <10 3 25+4 56

2m + 5 – 3m = 12 – 4m -3xy – 4y + 3x

Dividing Powers of the Same BaseClasswork

Simplify:

290. −4m4n3

m2n2291. 36 r

2 s6

4 r2 s3292. −12x

7 y11z3

8 x5 y3 z2

293. pq5 r5

p q3 r2294.

−14 x7 y3

−28 x4 y2295. −2g

3h8

16 gh5

296. −15 x2

25x2 y7297.

−26k5n4

13k4n3298.

−6m7n6 p18m4n3 p

299. −39 p4q3

3 p4q3300.

15m6n4

5m4n2

Dividing Powers of the Same BaseHomework

Simplify:

301. −15b5 c6

−12b2 c5302. 18 p q

4

−4 pq3303. m

7n5 p6

m3n2 p5


304. −4 r s7 t 3

12 r s6t 2305.

−18x6 y7

16 x3 y2306. 24 x

6 y12 z16x y6 z

307. 26 x5 y13

−2 x4 y7308.

g9h3

12g5h2309.

12g12h5 j6

18g10h2 j4

310. −18 j4k 5

−54 j4 k3

Spiral Review311. Solve: 312. Multiply: 313. Divide: 314. Solve:

-3(m + 2) – 2 = -3m – 4 1225∙ 246∙ 1518

2 34÷ 35

2(x + 3) – (4x – 3) ≤ -(x

– 3)

Power to a PowerClasswork

Simplify the following:315. (-5m3n3)3 316. (2x4yz6)2 317. (-3mn3p3)4

318. ( 2x4 y35 )3

319. (−3 r3s2 )3

320. (3x4y7)2

321. ( 5 x32 y2 z )4

322. (-7k3mn3)2 323. ( 3yz )5

324. (-2r2s6t)5

Power to a PowerHomework



325. (−4 r3 s23 )3

326. ( 2 xy3 z2 )3

327. (-3r2st6)4

328. (2x3y9z)3 329. (-3km3n2)5 330. ( 3 x4 z7y )3

331. (-6m3n5)2 332. ( 4 p2q4 )3

333. (-3x2yz5)3

334. (−5k33m2 )4

Spiral Review335. Solve: 336. Solve: 337. Subtract: 338. Evaluate,use m = 3, n = -4

-2(x + 5) – 3 = -3x 3m + 4 – 5m < - 2m + 3 3 25−2 14

5m – 2n + 3mn

Negative and Zero ExponentsClasswork

Write with positive exponents.

339. x-3y4z-6 340. -4m-3n-6p0 341. −3 r4 s−4

t−8342.

7 x5 y−7

−3w−4 z3

Write the following without a fraction.

343. −12m−4

3n−3 p5344.

1x4 y5 z−3

345. 36 a−3b4

−9c−6d−7 346. 45w3 x6

−5 y−8 z

Simplify where possible. Leave all answers with positive exponents.

347. −4 x−4 y3

12 x2 y5348. 27m

3n−8 p0

3m−5n−5 349. r−3 s6t−4

r−3 s−2 t7350. 36 x

−3 y−4

−14 x−6 y−9


Negative and Zero ExponentsHomework

Write with positive exponents.

351. 18 p2

−9q−2r−5352. r3s-2t0 353. −7 x

−4 y−6

z−3w−4 354. -9m-3n0p4

Write the following without a fraction.

3555. −36 x−3 y 4

4 z−5356. 24m

7n5

p−3q4357.

−3x4 y5 z3

358. −4 r3

s3 t7

Simplify where possible. Leave all answers with positive exponents.

359. −18 r0 s−4

36 r−4 s−2360. 45 x

−3 y4

−9 x7 y−3 361. −m−3n4 p−4

m−3n−5 p6362.

2 x−4 y−4

24 x−3 y−5

Spiral Review:363. Add: 364. Subtract: 365. Solve: 366. Multiply:

6 15+7 56 3 25

−2 13 2(3x – 2) – 4 = 2x + 5 (3x + 2)(4x – 1)

CombinationsClasswork

Simplify. Leave answer with positive exponents.

367. ( 16m3n24m3 p0 )3

368. (-3a-3b-2)-4 369. (2x3y-6)3

370. ( 4 x−3 y3

x−3 y 4 )−2

371. (−26 x3 y213 x5 y−12 )0

372. (3p-3q2r)3


373. (-2a-3b4)-2 374. −36 x4 y12

6 x10 y−2 375. ( 3 p3q64 p2 )−2

376. (3m-6n-3)-4

CombinationsHomework

Simplify. Leave answer with positive exponents.

377. (4x3y-4)-2 378. ( 16m−3n2

12m−4n6 )3

379. (-5x-12y7z-3)0

380. (5p3q-3m)2 381. (−72x−2 y−3

8 x6 y−5 )2

382. (-3m0n0p-6)-2

383. 42x6 y−4

84 x−2 y−3 384. (-5m-3p3q)-3 385. (−12 x3 y−4−18 x−2 y2 )−3

386. ( 14m3n47m−8n )2

Spiral Review387. Solve: 388. Factor: 389. Multiply: 390. Factor:4x – 7 – 7x > 2x – 9 x3 – 27y3 (2x + 5)(3x – 1) 16x2 – 1

Simplest Radical FormClasswork

Put the following into Simplest Radical Form:

391. −√36 392. −√81n2 393. 8√75 394. 5√800


395. 2 x√288 x3 396. 5√50 397. −5√45 x4 y5 398. −4√72

399. m2√48m7n9 400. 2√63 p12 401. a3√80a5 402. −3√125

Simplest Radical FormHomework

403. √16 404. −5√25 405. −3√704 406. √256m5

407. 4 x√32x9 408. 2 y √98 y6 409. −3√49 410. 8 pq√75 p3q2

411. √36 x4 y6 412. −4√225 y2 413. √100 414. √44 p5

Spiral Review:415. Work out: 416. Multiply: 417. Add: 418. Solve:

3 – 4(5 + 6) – 3(2)(5) 165

×203

×125

45+ 32 6x - 13 = -2x + 3

Adding and Subtracting RadicalsClasswork

Add or subtract. All answers must be left in simplest radical form.

419. 2√2+6√2 420. 6√2x−4√2 x 421. 8√5+5√5


422. 6 x √3−5 x√3 423. √2xy−√2xy 424. √18+√2

425. 6√3 x3−4 √27 x3 426. x √2+x √3+2 x √2 427. √5−√3+3√5

428. 3 x√48 x3+2 x2√12 x 429. 2√50−3√32 430. 4 x√20 y5−3√45 x2 y5

Adding and Subtracting RadicalsHomework

Add or subtract. All answers must be left in simplest radical form.

431. −√3+2√3 432. −√5+5√5 433. 10√7x−√7 x

434. 4 √12m2−2√3m2 435. 2 x√8 x2−x√2x2 436. 2√3+3√12

437. y √6 z3+ y √3 z3+2 y √6 z3 438. 4 √5 p−2√2 p+6√5 p439. 3√28+8√63

440. √18m3+√108m3−√50m3 441. √48 x4−√12 x4+√300 x 4442. 4 √20−3√45

Spiral Review443. Work out: 444. Subtract: 445. Solve: 446. Multiply:

-6 + 5(4) – 3(2 + 3) 83−34 6 – x – 3x = 30 (x + 4)(4x – 1)

Multiplying RadicalsClasswork

Multiply. All answers must be left in simplest radical form.

447. √3 ∙√5 448. √5 x ∙√6 x2 449. √5(√5+√3)


450. x √5 y3∙√5 y 451. 2√3 ∙7√5 452. 4 √10m3 ∙3√3m2

453. 8√5 xy ∙9 x√5 x4 454. 4 √5 p2 ∙3√15 p3 455. √2 (√3+√18 )

456. √3(√5+√27)

Multiplying RadicalsHomework

457. √10m3 ∙√13m5 458. √6(√2+√3) 459. √5(√7+√3)

460. x √3(√3 x2+ x√6) 461. √3(√15−√3) 462. 4 √2m3 ∙√6m

463. 5 r √10 s3 ∙3√10 r2 s5 464. √2 (√3+√8 ) 465. √3 (√12+√7 )

466. √2 (√8+√24 )

Spiral Review467. Work out: 468. Multiply: 469. Solve: 470. Divide:45÷53

+24÷32

45×205

×32 8b – 3(1 – b) = 6b – 4

365

÷ 45

Dividing RadicalsClasswork

Divide. All answers must be left in simplest radical form.


471. √54√6 472. √18√2 473. √42√7 474. √6 x√2x

475. 4√3 476. √35m

2

√3m477. √4a

√7a478. √ 25

479. √2√3

480. √ 40 x37 481. √40 x√8x

482. 3x√3

Dividing RadicalsHomework

Divide. All answers must be left in simplest radical form.

483. 1√2 484. √6 x

√5 x485. √5

√2486. √20 a

2

√5

487. √11√2

488. √27√3

489. √26

√13 x2 490. √ 54m

491. √ 37 492. √7√3 493. 2x√2 x 494. √ 2 x39

Spiral Review495. Work out: 496. Factor: 497. Multiply: 498. Factor:(10)(2) – (4)(3) + (3)(9) 25y2 – 64 (2x – 5)(2x + 5) 64x3 + 125

Review

Multiple Choice


1. 4x + 5 ≤ 2x – 3 is equivalent to:

a. x ≤ -4 b. x ≤ 1 c. x ≤ 4 d. x ≥ -4 e. x ≥ 4

2. If 225

= n500 , what is n equal to?

a. 2 b. 10 c. 20 d. 25 e. 40

3. Which of the following values of x makes this expression true: 54 < 3x?

a. 17 b. 18 c. 20 d. -54

4. If n + n + n = 216, what is the value of n?

a. 6 b. 36 c. 72 d. 74

5. What is the value of x if 10x – 15 = 5x + 20?

a. 1/3 b. 5 c. 7 d. 35

6. Simplify: √5 x√15x

a. 75x2

b. 75x c. 5 x√3 d. 25 x√3 e.3 x√5

7. Simplify: (-a2b3)3

a. a5b6 b. -a5b6 c. a6b9 d. -a6b9 e. -3a6b9

8. If x−38x=5, then x =

a. -10 b. -1 c. 1 d. 8 e. 43

9. Which expression is equivalent to the following equation: 2x – (5x – 3) = x + 7?

a. 10x + 6x = x + 7 b. 7x – 3 = x + 7 c. 7x + 3 = x + 7

d. -3x + 3 = x + 7 e. 3x – 3 = x + 7

10. Simplify: 4-2

a. -16 b. -8 c. −12

d. 116

e. 18

11. What is the exponent of x after (-4x3y2)2 is simplified?

a. 16 b. 9 c. 6 d. 3 e. 2


12. Simplify: x2 y6

x2 y2

a. y4 b. y3 c. xy3 d. xy4 e. x4y8

13. One of the solutions of the equation (x – 5)(3x + 4) = 0 is:

a. -5 b. −43

c. −34

d. 34

e. 43

14. One of the factors of x2 + x – 6 is

a. x + 3 b. x + 2 c. x + 1 d. x – 3 e. x – 6

15. Which of the following is a factor of 6x2 + 7x – 3?

a. (6x – 3) b. (3x – 1) c. (2x + 1) d. (3x + 3) e. (7x + 6)

16. √48−√12 is equal to:

a. 2√3 b. 12√3 c. 2 d. 6 e. 18

17. √50 is the same as:

a. 2√5 b. 5 c. 5√2 d. 10 e. 25

18. Solve: 2x3 – 9x2 + 9x = 0

a. 3,

32 , 0 b. -3,

−32, 0

c. −13, −32 d.

13, 23, 0

19. Which of the following is a factor of 2x2 + 7x + 6?

a. (2x + 3) b. (2x + 6) c. (x + 3) d. (2x + 7)

20. Simplify: √24 x4 y8 z3

a. 2 x2 y4 z √6 z b. 12 x4 y8√2 z c. 4 x2 y4√6 z3 d.

12 x4 y8 z √2 z


Short Answer – Additional Practice

Solve the following equations:

21. 2x - 1 = 5x + 3 22. 4x - 5 = 2x – 17

23. 8b – 3(1 – b) = 6b – 4 24. 19 – (2x + 3) = 2(x + 3) + x

25. 25x=45 26. 6x – 5 = 2x + 11 27.

x5+ 23=2 x4

−13

28. 6a + 2 = 4a – 8 29. -4 – b = -9(b – 8) - 2 30. 12x−23=34x+4

Solve the following inequalities:

31. 6a + 2 ≤ 4a – 8 32. 6 – x – 3x > 30

33. 4b – (3 – b) < 7b – 15 34. 8y – 3 – 9y ≥ 5 + 4y – 12

Factor out the GCF:

35. x2 + 7x 36. 3x2 + 9x 37. 12m3 – 4m2


38. 24x5 + 36x3 – 18x2 39. 16m4n3 – 12m3n4 + 4m2n5

Factor:40. x2 + 5x – 6 41. 3x2 + x – 2 42. 8x2 – 2x – 1

43. x2 – 2x – 15 44. 2m2 + 7m + 5 45. 10x2 +17x + 3

46. x3 - 27 47. 81x2 – 4y2 48. 2x2 – 11x + 12

49. 8m3 + n3 50. 6ab – 3b – 10a + 5 51. 2xy + 3x + 8y + 12

52. 3mn + 12m – 5n – 20 53. 3x3y – 6x2y – 45xy 54. 20m4 – 45m2

Find the solution for each equation by factoring. Show all work in the space provided.

55. 4x2 – 12x = 0 56. 3x2 + 9x = 0 57. x2 + 7x – 18 = 0

58. 2x2 = 19x + 33 59. 3 + 5x – 2x2 = 0 60. x3 – 2x2 – 3x = 0

61. x4 + 2x3 – 8x – 16 = 0 62. 6x3 – 22x2 – 8x = 0 63. 6x3 – 17x2 + 12x = 0

Simplify:

64. (m2n5)4 65. x2x5x 66.

a5b4

ab2 67. (3 x2 y4 )(−2xy )

68. ( -3x3y)2(2x)69. m3m4m3m 70. (xy)2(x3y) 71. (-3x3)(-4x5)


72. (3x2y3)3 73.

−6 x4 y7

−3 x3 y3 74. (−2a2b3 )4 75. (9 x

2 y )2

Simplify and write with Positive Exponents:

76. m-3 77. -4m0n-3 78. x-3y-2 79.

m−2 y−1

z−4

Simplify:

80. 3√ x+5√ x−4 √x 81. √3 x3 ∙√27 x 82. √24 x8 y7 83. √81x5 y8

84. −4√2x+5√3 x−14 √2 x 85. −4√2x ∙3√8 x5 86. 4√5

87. √48√12

88. 6√81x9 y12 89. 5√3x ∙4√6 x7 90. 5√3x+15√3 x−14√3x


Fundamental Skills of AlgebraClasswork and Homework Key

1. x = 12. m = 13. n = -64. p = -23/45. No Solution6. y = ¼7. x = 38. m = 5/29. p = -510. x = 511. x = -512. m = 313. x = 9/214. No Solution15. p = 1816. m = 117. k = 7/618. n = 319. x = -19/220. y = -3/421. 80

22. 3 1112

23.3160

24. 1925. x = -7/526. m = 2427. y = 13/3328. k = -165/229. m = -66/3530. k = -40/1131. x = -85/432. p = -100/333. m = 10/334. x = -2035. x = 536. m = -18/7

37. k = -26/3938. n = -100/339. y = 105/840. x = 2/741. x = -38/1142. y = 105/5243. p = -42/1144. m = 045. 19/1546. 5/6447. 648. -3049. b2 = c2 – a2

50. p=3 l+42m

51. k=m+1l

52. p=−6n−59

53. n= −1k−l

54. k=3 Aml

55. x= 3 y+26−4 y

56. m= 58n−1

57. m= 3 k5n2

58. k=m+23

59. k=5m−113

60. l= P−2w2


61. n=3M5m

62. p= 56k+l

63. m= 107n−8k

64. m= 45nl

65. l= 2k−23n−2m

66. p=a−10k1−b

67. p= 76ab−2

68. k=mn269. 8

70. 4 715

71.15215

72. -6373. x ≥ 2

74. m> 23

75. m≤− 811

76. m>2

77. x<−52

78. y ≥ 115

79. p< 193

80. k ≤−23

81. b← 10382. m≤3

83. x>−196

84. x≤1385. x>−1486. x≤−18

87. p≥ 35

88. m>145

89. m>−78

90. k ≥3091. m≥0

92. m>72

93. 994. 6

95.2027

96. 8297. 3ab (2a2+b )98. 4 am (m2+2m−1 )99. xy2(3y4 + 2y2 – 6)100. 3x2y(2xy – 1)101. 5p2q(2p – 3pq – q)102. 2m3n2(4mn + 6m – n)103. -2ab4(6a2 – 2a – 5)104. 7m3(n3 – n2 + 2)105. -3x3(2y2 – y – 2)106. 6m3n2(1 – 2m)107. 4x2y(2x – y)108. 4mn3(2m2 – m – 8)109. -3pq(6p2q – 1)110. -8x(y + 2 – x)111. p(2p5 + 3p3 + 1)112. 3m3n2(4m2 + 3mn + n2)113. -3p3(2p – 3q + 1)114. 2xy4(1 – 3x2 + 6x3)115. –x(x2y – x – 3)116. 2mn(6m2 – n – 1)117. a3b(a5 + a3b + b3)

118.6512

119.214

120. -12121. 267122. (x – 8)(x + 3)123. (a – 3b)(a – 2b)124. (y + 5)(y + 5)125. (m – 3n)(m + 2n)126. (x – y)(x – y)127. (a + 4b)(a – 3b)128. (p + 6)(p + 4)


129. (x – 4y)(x – 2y)130. (p – 10)(p – 3)131. (a + 3b)(a + 4b)132. (m – 6)(m + 4)133. (a - 12)(a – 1)134. (n + 3)(n – 2)135. (x – 7y)(x – 3y)136. (x + 9y)(x + 2y)137. (m – 5)(m + 1)138. (a + 8b)(a – 2b)139. (x – 10)(x – 2)140. (n + 3)(n + 4)141. (a – 9b)(a + 3b)142. 5

143.776

144.3356

145. 82146. (2x + 1)(x + 3)147. (3x – 2)(2x + 1)148. (5a – 3)(a + 4)149. (2m – n)(3m – n)150. (6p + 1)(p + 6)151. (3b – 2c)(4b + 3c)152. (m + 3)(4m + 5)153. (2c + 5d)(2c + 5d)154. (6m – 1)(2m – 3)155. (4m – 5p)(6m – 5p)156. (3x – 1)(2x – 1)157. (3p – 5)(5p + 1)158. (2m + 3)(5m – 1)159. (4x – y)(3x – y)160. (2p + 7)(2p + 5)161. (3m – 2n)(5m – n)162. (2p + 3)(p + 5)163. (x + y)(4x + y)164. (2p – 5)(3p – 5)165. (4m – n)(5m – n)166. 111

167.32

168. 157169. (a – 1)(a2 + a + 1)170. (5x – 4y)(5x + 4y)171. (11a – 4b)(11a + 4b)172. (3x + 2y)(9x2 + 6xy + 4y2)

173. (ab – c)(a2b2 + abc + c2)174. (2xy – 1)(2xy + 1)175. (6m – 5n)(6m + 5n)176. (2m + n)(4m2 – 2mn + n2)177. (a – 7)(a + 7)178. Not Factorable179. (y + 3)(y2 – 3y + 9)180. (4m – 1)(16m2 + 4m + 1)181. (p – 6q)(p + 6q)182. (mn – 2)(mn + 2)183. Not Factorable184. (2x – 3y)(4x2 + 6xy + 9y2)185. (p – qr)(p2 + pqr + q2r2)186. (5m – 1)(25m2 + 5m + 1)187. (5x – 9)(5x + 9)188. (10x – y)(10x + y)189. 10190. 13191. -22192. -2193. (x + 4)(2y + 5)194. (3m – 5)(3n – 1)195. (2x – 3)(y – 5)196. (5r + 3)(2s – 5)197. (2p – 1)(5q – 1)198. (5m + 3)(2n + 1)199. (x + z)(y – 1)200. (2k – 9)(m + 7)201. (z + 4)(x – y)202. (3 – 4y)(2x + 5)203. (2m – 5)(3p – 1)204. (3x + 2)(2y + 5)205. (4r + 3)(s – 1)206. (3t – 1)(2r – 3)207. (4m + 3)(2n + 1)208. (x – 5)(3y – 4)209. (m – 1)(n – 1)210. (3q – 4)(2r + 5)211. (5m – 3)(2m – 3)212. (3p – 4)(3q – 4)

213. 8 1315

214.196

215.24175


216.11465

217. 3x(x – 3)(x – 4)218. 2m(3m – 1)(m + 1)219. 3ab(a – 4)(a + 4)220. 2x(3x + y)(9x2 – 3xy + y2)221. x2y(x + 10)(x + 2)222. -3mn(2m – 1)(m + 4)223. 4pq(p – 4)(q – 3)224. -2x3(2x + y)(4x2 – 2xy + y2)225. -5m2n(m – 3)(2m – 1)226. 4p(5p – 4q)(5p + 4a)227. 3m(m – n)(m + n)228. -2x(3x – 1)(x + 5)229. 2ab(3a – 5)(3a + 5)230. xy(x + 3)(x2 – 3x + 9)231. -3r(4r + 3)(r + 1)232. 2xy(x – 1)(y – 1)233. mn(2m – n)(3m – n)234. –pq(p – q)(p + q)235. 10(3x + 4)(2x + 5)236. -4mn(2m + 1)(m + 1)237. 32238. 227

239. 7 3135

240. 16241. x = 0, 4, -4

242. x=1 ,−32

243. m=0 ,−5 ,−6

244. r=12,−52

245. x=6 ,7246. p = 0, -1, -3

247. r=0 , 72,−2

248. y = 0, 4, -5

249. x=0 , 13,−5

250. m = 0, 1, -3251. x = 0, 6, 4252. m = 0, -4, -8253. p = 0, 8, -8

254. m=0 ,−12,−43

255. k=0 ,3 , 13

256. p=0 , 12,−12

257. r=52, 13

258. x=8 , 32

259. x=0 , 32,−32

260. k=0 ,−52,6

261. -66262. x = 3263. (5x – 6)(5x + 6)

264. x←253

265. x6y6

266. -8m4n8

267. -21x7y5

268. 12p4q6

269. 15m2n2p4

270. 20k5r9

271. -24x9y3z10

272. 12p4q11

273. -15r8s6

274. -10x2y8

275. -12x5y6

276. -6m5n7

277. 36r10s7

278. -10x3y15z5

279. 20r4s13

280. –m5n9p4

281. 12p2q4r6

282. 8m4n5

283. 28x4y5

284. 12m10n19

285. -12x5y9

286. x > 7

287. 8 730

288. m=73

289. 12290. -4m2n291. 9s3


292. −3 x2 y8 z2

293. q2r3

294. x3 y2

295. −g2h3

8

296.−35 y7

297. −2kn

298. −m3n3

3299. −¿13300. 3m2n2

301. 5b3 c4

302.−9q2

303. m4n3 p

304.−st3

305. −9 x3 y5

8

306. 3x5 y6

2307. -13xy6

308. g4h12

309. 2g2h3 j2

3

310. k2

3311. No Solution

312.85

313.5512

314. x ≥ 6315. -125m9n9

316. 4x8y2z12

317. 81m4n12p12

318. 8 x12 y9

125

319. −27 r9

s6

320. 9 x8 y14

321.625x12

16 y8 z4

322. 49 k6n2n6

323.243y5 z5

324. −32 r10 s30 t5

325. −64 r9 s6

27

326.8 x3

y9 z6

327. 81 r8 s4 t24

328. 8 x9 y27 z3

329. −243m15n10

330. 27 x12 z21

y3

331. 36m6n10

332.64 p6

q12

333. −27 x6 y3 z15

334.625 k12

81m8335. x=13336. No Solution

337. 1 320

338. −13

339.y4

x3 z6

340.−4m3n6

341. −3 r4 t 8

s4

342.−7 x5w4

3 y7 z3343. -4m-4n-3p-5

344. x-4y-5z3

345. -4a-3b4c6d7

346. -9w3x6y8z-1

347.−13x6 y2


348. 9m8

n3

349.s8

t11

350. −18x3 y5

7351. -2p2q2r5

352. r3

s2

353.−7w 4 z3

x4 y6

354.−9 p4

m3355. -9x-3y4z5

356. 24m7n5p3q-4

357. -3x-4y-5z-3

358. -4r3s-3t-7

359. −r4

2 s2

360.−5 y7

x10

361.−n9

p10

362.y12x 6

363. 14 130

364.1615

365. x=134

366. 12 x2+5 x−2367. 64n6

368. a12b8

81

369.8a9

y18

370. y2

16371. 1

372. 27q6 r3

p9

373. a6

4b8

374.−6 y14

x6

375.16

9 p2q12

376. m24n12

81

377.y8

16x6

378.64m3

27n12379. 1

380. 25 p6m2

q6

381.81 y 4

x8

382. p12

9

383. x8

2 y

384.−m9

125 p9q3

385.27 y18

8 x15

386. 4m22n6

387. x< 25

388. (x – 3y)(x2 + 3xy + 9y2)389. 6x2 + 13x – 5390. (4x – 1)(4x + 1)391. -6392. -9n393. 40 √3394. 100√2395. 24 x2√2 x396. 25√2397. −15 x2 y2√5 y398. −24 √2399. 4m5n4√3mn400. 6 p6√7401. 4 a5√5 a402. −15√5


403. 4404. -25405. −24 √11406. 16m2√m407. 16 x5√2 x408. 14 y4√2409. −21410. 40 p2q2√3 p411. 6 x2 y3412. −60 y413. 10414. 2 p2√11 p415. -71

416.2565

417.2310

418. x = 2419. 8√2420. 2√2 x421. 13√5422. x √3423. 0424. 4 √2425. −6 x √3 x426. 3 x√2+x √3427. 4 √5−√3428. 16 x2√3 x429. −2√2430. −x y2√5 y431. √3432. 4 √5433. 9√7 x434. 6m√3435. 3 x2√2436. 8√3437. 3 yz √6 z+ yz √3 z438. 10√5 p−2√2 p439. 30√7440. 6m√3m−2m√2m441. 12 x2√3442. −√5443. −¿1

444.2312

445. x = -6446. 4x2 + 15x – 4447. √15448. x √30 x449. 5+√15450. 5 x y2

451. 14√15452. 12m2√30m453. 360 x3√ xy454. 60 p2√3 p455. √6+6456. √15+3457. m4√130458. 2√3+3√2459. √35+√15460. 3 x2+3 x2√2461. 3√5−3462. 8m2√3463. 150r2s4

464. √6+4465. 6+√21466. 4+4√3467. 7

468.245

469. b=−15

470. 9471. 3472. 3473. √6474. 2

475. 4 √33

476. √105m3

477. 2√77

478. √105

479. √63

480. 2x √70 x7

481. √5


482. x √3483. √2

2

484. √305

485. √102

486. 2a

487. √222

488. 3489. √2/ x

490. √5m2m

491. √217

492. √213

493. √2x494. x√2x

3495. 35496. (5y – 8)(5y + 8)497. 4x2 – 25498. (4x + 5)(16x2 – 20x + 25)

Answers to Review1. A2. E3. C4. C5. C6. C7. D8. D9. D10. D11. C12. A13. B14. A15. B16. A17. C18. A19. A20. A

21. x=−43

22. x=−¿623. b=−¿1/524. x=2

25. x=2252

26. x=4

27. x=10328. a=−5

29. b=748

30. x=−563

31. a≤−532. x < -633. b > 6

34. y ≤ 4535. x (x+7 )36. 3x(x + 3)37. 4m2(3m – 1)38. 6x2(4x3 + 6x – 3)39. 4m2n3(4m2 – 3mn +

n2)40. (x + 3)(x – 2)41. (x + 1)(3x – 2)42. (2x – 1)(4x + 1)43. (x – 5)(x + 3)44. (2m + 5)(m + 1)45. (2x + 3)(5x + 1)46. (x – 3)(x2 + 3x + 9)47. (9x – 2y)(9x + 2y)

48. (x – 4)(2x – 3)49. (2m + n)(4m2 – 2mn

+ n2)50. (3b – 5)(2a – 1)51. (x + 4)(2y + 3)52. (3m – 5)(n + 4)53. 3xy(x – 5)(x + 2)54. 5m2(2m – 3)(2m + 3)55. x = 0, 356. x = 0, -357. x = -9, 2

58. x=11 ,−32

59. x=3 ,−1260. x=0 ,3 ,−161. x = 2, -2

62. x=0 ,4 ,−13

63. x=0 , 32, 43

64. m8n20

65. x8

66. a4b2

67. -6x3y4

68. 18x7y2

69. m11


70. x5y3

71. 12x8

72. 27x6y9

73. 2xy4

74. 16a8b12

75. 81x4y2

76.1m3

77.−4n3

78.1x3 y2

79.z4

m2 y80. 4 √x81. 81x2

82. 2 x4 y3√6 y

83. 9 x2 y 4√x84. −18√2x+5√3 x85. −48x3

86. 4 √55

87. 288. 9 x4 y6√x89. 60 x4√290. 6√3 x


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