Solving Equations

Classwork

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) – 44. 2(p + 4) – 8 = -2(p + 9) – 5

5. 5x – 3 – 2x – 8 = 3x – 4 + 26. 8y – 10 + 4 = 6y – 2y – 5

7. 4 – (x – 8) = 3 + 2x8. 3 – 2(m + 4) = 5 – 6m

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

Solving Equations

Homework

Solve the following equations. Show all work.

11. 2x – 8x – 4 + 3 = -5x + 412. 3(m – 9) + 2(m + 3) = -6

13. 4x + 5 – 8x + 10 = 2x – 1214. 4(x + 6) – 10 = 2(2x – 3)

15. 5p + 12 – 8 + 2p = 6(p + 4) – 216. 2(m + 3) – 4 = 5(m + 1) – 6

17. 6(k – 3) – (k – 4) = -(k + 6) – 118. 5(2n – 5) – 3 = 2(3n – 4) – 8

19. 4(x – 12) – 6x = 2x – 1020. 3y – 10 – 11y – 6 = -4y – 13

Spiral Review

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

10 × 24 ÷ 3 × 12 6 + (3p ÷ 4) + 2q

Equations with Fractions

Classwork

Solve the following equations. Show all work.

25. 26.

27. 28.

29. 30.

31. 32.

33. 34.

Equations with Fractions

Homework

Solve the following equations. Show all work.

35. 36.

37. 38.

39. 40.

41. 42.

43. 44.

Spiral Review

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

[(-17) – (8-1)] ÷ (-4) p(q ÷ 3 – p)

Formulas

Classwork

Solve the following formulas for the specified variable:

49. a2 + b2 = c2 for b250.

51. 52. 5p + 6n = -4p – 5 for p

53. 54.

55. 6x – 3y = 4xy + 2 for x56. 8mn – m = 5 for m

57. 58. 6k + 2 – m = 3k + 4 for k

Formulas

Homework

Solve the following formulas for the specified variable:

59. 3(k + 4) = 5m + 1 for k60.

61. 62.

63. 7mn – 8 = 8mk + 2 for m64.

65. 66. 10k + p = a + bp for p

67. 6abp – 2p = 7 for p68.

Spiral Review

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

[(-28) × 2) ÷ ((-8) – (-1)] 1 + 4(2 – 3k)

Solving Inequalities

Classwork

Solve the following Inequalities. Show all work.

73. 3x – 4 ≥ -2x + 674. 2m – 7< 5m – 9

75. 3(m – 4) ≤ -8(m + 2) – 476. –(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 + 1282. 6(2m – 3) – 4 ≤ 6m – 4

Solving Inequalities

Homework

Solve the following Inequalities. Show all work.

83. 2x – 12 < 8x + 784. 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 – 5p88. -3(m – 4) – (m – 3) < m + 1

89. -6m – 9 – 4 < 2m + 3 – 990. 5(k – 3) – 2(k + 4) ≥ 2k + 7

91. 3(2m – 5) + 7 ≤ 4(2m – 3) + 492. 10m – 7 – 3m – 5 > 6m – 3m + 2

Spiral Review

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

(-26 + 8) ÷ (-6 + 4) -2(-6x – 9) + 4

Factoring out the GCF

Classwork

Factor out the GCF from the following:

97. 6a3b + 3ab298. 4am3 + 8am2 – 4am99. 3xy6 + 2xy4 – 6xy2

100. 6x3y2 – 3x2y 101. 10p3q – 15p3q2 – 5p2q2102. 8m4n3 + 12m4n2 – 2m3n3

103. -12a3b4 + 4a2b4 + 10ab4104. 7m3n3 – 7m3n2 + 14m3105. -6x3y2 + 3x3y + 6x3

106. 6m3n2 – 12m4n2

Factoring out the GCF

Homework

Factor out the GCF from the following:

107. 8x3y – 4x2y2108. 8m3n3 – 4m2n3 – 32mn3109. -18p3q2 + 3pq

110. -8xy – 16x + 8x2111. 2p6 + 3p4 + p112. 12m5n2 + 9m4n3 + 3m3n4

113. -6p4 + 9p3q – 3p3114. 2xy4 – 6x3y4 + 12x4y4115. –x3y + x2 + 3x

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

Spiral Review

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

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

Factoring x2 + bx + c

Classwork

Factor the following:

122. x2 – 5x – 24123. a2 – 5ab + 6b2 124. y2 + 10y + 25

125. m2 – mn – 6n2126. x2 – 2xy + y2127. a2 + ab – 12b2

128. p2 + 10p + 24129. x2 – 6xy + 8y2130. p2 – 13p + 30

131. a2 + 7ab + 12b2

Factoring x2 + bx + c

Homework

Factor the following:

132. m2 – 2m – 24133. a2 – 13a + 12134. n2 + n – 6

135. x2 – 10xy + 21y2136. x2 + 11xy + 18y2137. m2 – 4m – 5

138. a2 + 6ab – 16b2139. x2 – 12x + 20140. n2 + 7n + 12

141. a2 – 6ab – 27b2

Spiral Review

142. Work out:143. Multiply:144. Divide145. Evaluate, use x = 5:

5 – 4 [(-2) – (-2)] -2(-6x – 9) + 4

Factoring ax2 + bx + c

Classwork

146. 2x2 + 7x + 3147. 6x2 – x – 2148. 5a2 + 17a – 12

149. 6m2 - 5mn + n2150. 6p2 + 37p + 6151. 12b2 + bc – 6c2

152. 4m2 + 17m + 15153. 4c2 + 20cd + 25d2154. 12m2 – 20m + 3

155. 24m2 – 50mp + 25p2

Factoring ax2 + bx + c

Homework

156. 6x2 – 5x + 1157. 15p2 – 22p – 5 158. 10m2 + 13m – 3

159. 12x2 – 7xy + y2160. 4p2 + 24p + 35 161. 15m2 – 13mn + 2n2

162. 2p2 + 13p + 15163. 4x2 + 5xy + y2 164. 6p2 – 25p + 25

165. 20m2 – 9mn + n2

Spiral Review

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

(52 – 1) × 4 + 33 – (4 + 8) 1 – 4(2 – 3k)+ 3k2 – 2k – 4

Factoring a2 – b2, a3 – b3, a3 + b3

Classwork

Factor the following:

169. a3 – 1170. 25x2 – 16y2171. 121a2 – 16b2

172. 27x3 + 8y3173. a3b3 – c3174. 4x2y2 – 1

175. 36m2 – 25n2176. 8m3 + n3177. a2 – 49

178. 4x2 + 25

Factoring a2 – b2, a3 – b3, a3 + b3

Homework

Factor the following:

179. y3 + 27180. 64m3 – 1181. p2 – 36q2

182. m2n2 – 4183. x2 + 16184. 8x3 – 27y3

185. p3 – q3r3186. 125m3 – 1187. 25x2 – 81

188. 100x2 – y2

Spiral Review

189. Work out:190. Simplify:191. Work out:192. Evaluate, use x = 1, z = 6

10 × [(-10) + 1] ÷ (-9) 3 – 5 [(-3) – (-1)] (-3) – (-6) - 52z ÷ 6 + x + x – 5

Factoring by Grouping

Classwork

Factor the following by grouping:

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

195. 2xy – 10x – 3y + 15196. 10rs – 25r + 6s – 15

197. 10pq – 2p – 5q + 1198. 10mn + 5m + 6n + 3

199. xy – x + zy – z200. 2km + 14k – 9m – 63

201. zx – zy + 4x – 4y202. 6x + 15 – 8xy – 20y

Factoring by Grouping

Homework

Factor the following by grouping:

203. 6mp – 2m – 15p + 5204. 6xy + 15x + 4y + 10

205. 4rs – 4r + 3s – 3206. 6tr – 9t – 2r + 3

207. 8mn + 4m + 6n + 3208. 3xy – 4x – 15y + 20

209. mn – m – n + 1210. 6qr + 15q – 8r – 20

211. 10mn – 15m – 6n + 9212. 9pq – 12p – 12q + 16

Spiral Review

213. Add:214. Subtract:215. Multiply:216. Divide:

Factoring Completely

Classwork

Factor each of the following as much as possible.

217. 3x3 – 12x2 + 36x218. 6m3 + 4m2 – 2m219. 3a3b – 48ab

220. 54x4 + 2xy3221. x4y + 12x3y + 20x2y222. -6m3n – 21m2n + 12mn

223. 4p2q2 – 12p2q – 16pq2 + 48pq224. -16x6 – 2x3y3225. -10m4n + 35m3n – 15m2n

226. 100p3 – 64pq2

Factoring Completely

Homework

Factor each of the following as much as possible.

227. 3m3 – 3mn2228. -6x3 – 28x2 + 10x229. 18a3b – 50ab

230. x4y + 27xy231. -12r3 – 21r2 – 9r232. 2x2y2 – 2x2y – 2xy2 + 2xy

233. 6m3n – 5m2n2 + mn2234. –p3q + pq3235. 60x2 + 230x + 200

236. -8m3n – 12m2n – 4mn

Spiral Review

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

8(-4)  (2)(-1) + (4)2 172 - (12 - 4)2 + 2 -3x + 2y – xy + x

Solving by Factoring

Classwork

Solve the following equations by factoring:

241. x3 – 16x = 0242. 2x2 + x – 3 = 0243. m3 + 11m2 + 30m = 0

244. 4r2 = -8r + 5245. x2 + 42 = 13x246. 12p2 + 9p = -3p3

247. 2r3 = 14r + 3r2248. 4y3 + 4y2 = 80y249. 5x = 3x3 + 14x2

250. m3 + 2m2= 3m

Solving by Factoring

Homework

Solve the following equations by factoring:

251. 2x3 – 20x2 + 48x = 0252. 3m3 + 36m2 + 96n = 0253. 2p3 = 128p

254. 6m3 + 5m2 = 4m255. 3k3 + 3k = 10k2256. 16p3 = 4p

257. 6r2 + 5 = 17r258. 2x2 + 24 = 19x259. 4x3 – 9x = 0

260. 6k3 = 21k2 + 90k

Spiral Review

261. Work out:262. Solve:263. Factor:264. Solve:

4 – 5(2 + 3(4))2x + 3x – 7 = x + 5 25x2 – 364(x – 5) – (3x + 3) > 4x + 2

Multiplying Powers of the Same Base

Classwork

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)

MultiplingPowers of the Same Base

Homework

Simplify the following:

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 Review

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

2(x + 4) – 3(x – 3) <10 2m + 5 – 3m = 12 – 4m -3xy – 4y + 3x

Dividing Powers of the Same Base

Classwork

Simplify:

290. 291.292.

293. 294. 295.

296. 297. 298.

299. 300.

Dividing Powers of the Same Base

Homework

Simplify:

301. 302.303.

304. 305. 306.

307. 308. 309.

310.

Spiral Review

311. Solve:312. Multiply:313. Divide:314. Solve:

-3(m + 2) – 2 = -3m – 4 2(x + 3) – (4x – 3) ≤ -(x – 3)

Power to a Power

Classwork

Simplify the following:

315. (-5m3n3)3316. (2x4yz6)2317. (-3mn3p3)4

318. 319. 320. (3x4y7)2

321. 322. (-7k3mn3)2323.

324. (-2r2s6t)5

Power to a Power

Homework

Simplify the following:

325. 326. 327. (-3r2st6)4

328. (2x3y9z)3329. (-3km3n2)5330.

331. (-6m3n5)2332. 333. (-3x2yz5)3

334.

Spiral Review

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

-2(x + 5) – 3 = -3x 3m + 4 – 5m < - 2m + 3 5m – 2n + 3mn

Negative and Zero Exponents

Classwork

Write with positive exponents.

339. x-3y4z-6340. -4m-3n-6p0341. 342.

Write the following without a fraction.

343. 344. 345. 346.

Simplify where possible. Leave all answers with positive exponents.

347. 348. 349. 350.

Negative and Zero Exponents

Homework

Write with positive exponents.

351. 352. r3s-2t0353. 354. -9m-3n0p4

Write the following without a fraction.

3555. 356. 357. 358.

Simplify where possible. Leave all answers with positive exponents.

359. 360. 361. 362.

Spiral Review:

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

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

Combinations

Classwork

Simplify. Leave answer with positive exponents.

367. 368. (-3a-3b-2)-4369. (2x3y-6)3

370. 371. 372. (3p-3q2r)3

373. (-2a-3b4)-2374. 375.

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

Combinations

Homework

Simplify. Leave answer with positive exponents.

377. (4x3y-4)-2378. 379. (-5x-12y7z-3)0

380. (5p3q-3m)2381. 382. (-3m0n0p-6)-2

383. 384. (-5m-3p3q)-3385.

386.

Spiral Review

387. Solve:388. Factor:389. Multiply:390. Factor:

4x – 7 – 7x > 2x – 9 x3 – 27y3 (2x + 5)(3x – 1) 16x2 – 1

Simplest Radical Form

Classwork

Put the following into Simplest Radical Form:

391. 392. 393. 394.

395. 396. 397. 398.

399. 400. 401. 402.

Simplest Radical Form

Homework

403. 404. 405. 406.

407. 408. 409. 410.

411. 412. 413. 414.

Spiral Review:

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

3 – 4(5 + 6) – 3(2)(5) 6x - 13 = -2x + 3

Adding and Subtracting Radicals

Classwork

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

419. 420. 6421. 8

422. 423. 424.

425. 426. 427.

428. 429. 430.

Adding and Subtracting Radicals

Homework

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

431. 432. 433.

434. 435. 436.

437. 438. 439.

440. 441. 442.

Spiral Review

443. Work out:444. Subtract:445. Solve:446. Multiply:

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

Multiplying Radicals

Classwork

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

447. 448. 449.

450. 451. 452.

453. 454. 455.

456.

Multiplying Radicals

Homework

457. 458. 459.

460. 461. 462.

463. 464. 465.

466.

Spiral Review

467. Work out:468. Multiply:469. Solve:470. Divide:

8b – 3(1 – b) = 6b – 4

Dividing Radicals

Classwork

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

471. 472. 473. 474.

475. 476. 477. 478.

479. 480. 481. 482.

Dividing Radicals

Homework

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

483. 484. 485. 486.

487. 488. 489. 490.

491. 492. 493. 494.

Spiral Review

495. 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 ≤ -4b. x ≤ 1c. x ≤ 4 d. x ≥ -4e. x ≥ 4

2. If , what is n equal to?

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

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

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

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

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

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

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

6. Simplify:

a. b. 75xc. d. e.

7. Simplify:(-a2b3)3

a. a5b6b. -a5b6c. a6b9d. -a6b9e. -3a6b9

8. If , then x =

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

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

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

d. -3x + 3 = x + 7e. 3x – 3 = x + 7

10. Simplify: 4-2

a. -16b. -8c. d. e.

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

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

12. Simplify:

a. y4b. y3c. xy3d. xy4e. x4y8

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

a. -5b. c. d. e.

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

a. x + 3b. x + 2c. x + 1d. x – 3e. 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. is equal to:

a. b. c. 2 d. 6 e. 18

17. is the same as:

a. 2 b. 5 c. 5 d. 10e. 25

18. Solve: 2x3 – 9x2 + 9x = 0

a. 3, , 0b. -3, c. d.

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:

a. b. c. d.

Short Answer – Additional Practice

Solve the following equations:

21. 2x - 1 = 5x + 322. 4x - 5 = 2x – 17

23. 8b – 3(1 – b) = 6b – 424. 19 – (2x + 3) = 2(x + 3) + x

25. 26. 6x – 5 = 2x + 1127.

28. 6a + 2 = 4a – 829. -4 – b = -9(b – 8) - 230.

Solve the following inequalities:

31. 6a + 2 ≤ 4a – 832. 6 – x – 3x > 30

33. 4b – (3 – b) < 7b – 1534. 8y – 3 – 9y ≥ 5 + 4y – 12

Factor out the GCF:

35. x2 + 7x36. 3x2 + 9x37. 12m3 – 4m2

38. 24x5 + 36x3 – 18x239. 16m4n3 – 12m3n4 + 4m2n5

Factor:

40. x2 + 5x – 641. 3x2 + x – 242. 8x2 – 2x – 1

43. x2 – 2x – 1544. 2m2 + 7m + 545. 10x2 +17x + 3

46. x3 - 2747. 81x2 – 4y248. 2x2 – 11x + 12

49. 8m3 + n350. 6ab – 3b – 10a + 551. 2xy + 3x + 8y + 12

52. 3mn + 12m – 5n – 2053. 3x3y – 6x2y – 45xy54. 20m4 – 45m2

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

55. 4x2 – 12x = 056. 3x2 + 9x = 057. x2 + 7x – 18 = 0

58. 2x2 = 19x + 3359. 3 + 5x – 2x2 = 060. x3 – 2x2 – 3x = 0

61. x4 + 2x3 – 8x – 16 = 062. 6x3 – 22x2 – 8x = 063. 6x3 – 17x2 + 12x = 0

Simplify:

64. (m2n5)465. x2x5x 66. 67.

68. ( -3x3y)2(2x)69. m3m4m3m70. (xy)2(x3y)71. (-3x3)(-4x5)

72. (3x2y3)3 73. 74. 75.

Simplify and write with Positive Exponents:

76. m-377. -4m0n-378. x-3y-279.

Simplify:

80. 81. 82. 83.

84. 85. 86. 87.

88. 89. 90.

Fundamental Skills of Algebra

Classwork and Homework Key

Alg. II – Fund. Skills~1~NJCTL.org

  1. x = 1
  2. m = 1
  3. n = -6
  4. p = -23/4
  5. No Solution
  6. y = ¼
  7. x = 3
  8. m = 5/2
  9. p = -5
  10. x = 5
  11. x = -5
  12. m = 3
  13. x = 9/2
  14. No Solution
  15. p = 18
  16. m = 1
  17. k = 7/6
  18. n = 3
  19. x = -19/2
  20. y = -3/4
  21. 80
  22. 19
  23. x = -7/5
  24. m = 24
  25. y = 13/33
  26. k = -165/2
  27. m = -66/35
  28. k = -40/11
  29. x = -85/4
  30. p = -100/3
  31. m = 10/3
  32. x = -20
  33. x = 5
  34. m = -18/7
  35. k = -26/39
  36. n = -100/3
  37. y = 105/8
  38. x = 2/7
  39. x = -38/11
  40. y = 105/52
  41. p = -42/11
  42. m = 0
  43. 19/15
  44. 5/64
  45. 6
  46. -30
  47. b2 = c2 – a2
  48. -63
  49. x ≥ 2
  50. 6
  51. 82
  52. xy2(3y4 + 2y2 – 6)
  53. 3x2y(2xy – 1)
  54. 5p2q(2p – 3pq – q)
  55. 2m3n2(4mn + 6m – n)
  56. -2ab4(6a2 – 2a – 5)
  57. 7m3(n3 – n2 + 2)
  58. -3x3(2y2 – y – 2)
  59. 6m3n2(1 – 2m)
  60. 4x2y(2x – y)
  61. 4mn3(2m2 – m – 8)
  62. -3pq(6p2q – 1)
  63. -8x(y + 2 – x)
  64. p(2p5 + 3p3 + 1)
  65. 3m3n2(4m2 + 3mn + n2)
  66. -3p3(2p – 3q + 1)
  67. 2xy4(1 – 3x2 + 6x3)
  68. –x(x2y – x – 3)
  69. 2mn(6m2 – n – 1)
  70. a3b(a5 + a3b + b3)
  71. -12
  72. 267
  73. (x – 8)(x + 3)
  74. (a – 3b)(a – 2b)
  75. (y + 5)(y + 5)
  76. (m – 3n)(m + 2n)
  77. (x – y)(x – y)
  78. (a + 4b)(a – 3b)
  79. (p + 6)(p + 4)
  80. (x – 4y)(x – 2y)
  81. (p – 10)(p – 3)
  82. (a + 3b)(a + 4b)
  83. (m – 6)(m + 4)
  84. (a - 12)(a – 1)
  85. (n + 3)(n – 2)
  86. (x – 7y)(x – 3y)
  87. (x + 9y)(x + 2y)
  88. (m – 5)(m + 1)
  89. (a + 8b)(a – 2b)
  90. (x – 10)(x – 2)
  91. (n + 3)(n + 4)
  92. (a – 9b)(a + 3b)
  93. 5
  94. 82
  95. (2x + 1)(x + 3)
  96. (3x – 2)(2x + 1)
  97. (5a – 3)(a + 4)
  98. (2m – n)(3m – n)
  99. (6p + 1)(p + 6)
  100. (3b – 2c)(4b + 3c)
  101. (m + 3)(4m + 5)
  102. (2c + 5d)(2c + 5d)
  103. (6m – 1)(2m – 3)
  104. (4m – 5p)(6m – 5p)
  105. (3x – 1)(2x – 1)
  106. (3p – 5)(5p + 1)
  107. (2m + 3)(5m – 1)
  108. (4x – y)(3x – y)
  109. (2p + 7)(2p + 5)
  110. (3m – 2n)(5m – n)
  111. (2p + 3)(p + 5)
  112. (x + y)(4x + y)
  113. (2p – 5)(3p – 5)
  114. (4m – n)(5m – n)
  115. 111
  116. 157
  117. (a – 1)(a2 + a + 1)
  118. (5x – 4y)(5x + 4y)
  119. (11a – 4b)(11a + 4b)
  120. (3x + 2y)(9x2 + 6xy + 4y2)
  121. (ab – c)(a2b2 + abc + c2)
  122. (2xy – 1)(2xy + 1)
  123. (6m – 5n)(6m + 5n)
  124. (2m + n)(4m2 – 2mn + n2)
  125. (a – 7)(a + 7)
  126. Not Factorable
  127. (y + 3)(y2 – 3y + 9)
  128. (4m – 1)(16m2 + 4m + 1)
  129. (p – 6q)(p + 6q)
  130. (mn – 2)(mn + 2)
  131. Not Factorable
  132. (2x – 3y)(4x2 + 6xy + 9y2)
  133. (p – qr)(p2 + pqr + q2r2)
  134. (5m – 1)(25m2 + 5m + 1)
  135. (5x – 9)(5x + 9)
  136. (10x – y)(10x + y)
  137. 10
  138. 13
  139. -22
  140. -2
  141. (x + 4)(2y + 5)
  142. (3m – 5)(3n – 1)
  143. (2x – 3)(y – 5)
  144. (5r + 3)(2s – 5)
  145. (2p – 1)(5q – 1)
  146. (5m + 3)(2n + 1)
  147. (x + z)(y – 1)
  148. (2k – 9)(m + 7)
  149. (z + 4)(x – y)
  150. (3 – 4y)(2x + 5)
  151. (2m – 5)(3p – 1)
  152. (3x + 2)(2y + 5)
  153. (4r + 3)(s – 1)
  154. (3t – 1)(2r – 3)
  155. (4m + 3)(2n + 1)
  156. (x – 5)(3y – 4)
  157. (m – 1)(n – 1)
  158. (3q – 4)(2r + 5)
  159. (5m – 3)(2m – 3)
  160. (3p – 4)(3q – 4)
  161. 3x(x – 3)(x – 4)
  162. 2m(3m – 1)(m + 1)
  163. 3ab(a – 4)(a + 4)
  164. 2x(3x + y)(9x2 – 3xy + y2)
  165. x2y(x + 10)(x + 2)
  166. -3mn(2m – 1)(m + 4)
  167. 4pq(p – 4)(q – 3)
  168. -2x3(2x + y)(4x2 – 2xy + y2)
  169. -5m2n(m – 3)(2m – 1)
  170. 4p(5p – 4q)(5p + 4a)
  171. 3m(m – n)(m + n)
  172. -2x(3x – 1)(x + 5)
  173. 2ab(3a – 5)(3a + 5)
  174. xy(x + 3)(x2 – 3x + 9)
  175. -3r(4r + 3)(r + 1)
  176. 2xy(x – 1)(y – 1)
  177. mn(2m – n)(3m – n)
  178. –pq(p – q)(p + q)
  179. 10(3x + 4)(2x + 5)
  180. -4mn(2m + 1)(m + 1)
  181. 32
  182. 227
  183. x = 0, 4, -4
  184. p = 0, -1, -3
  185. y = 0, 4, -5
  186. m = 0, 1, -3
  187. x = 0, 6, 4
  188. m = 0, -4, -8
  189. p = 0, 8, -8
  190. -66
  191. x = 3
  192. (5x – 6)(5x + 6)
  193. x6y6
  194. -8m4n8
  195. -21x7y5
  196. 12p4q6
  197. 15m2n2p4
  198. 20k5r9
  199. -24x9y3z10
  200. 12p4q11
  201. -15r8s6
  202. -10x2y8
  203. -12x5y6
  204. -6m5n7
  205. 36r10s7
  206. -10x3y15z5
  207. 20r4s13
  208. –m5n9p4
  209. 12p2q4r6
  210. 8m4n5
  211. 28x4y5
  212. 12m10n19
  213. -12x5y9
  214. x > 7
  215. -4m2n
  216. 9s3
  217. 13
  218. -13xy6
  219. No Solution
  220. x ≥ 6
  221. -125m9n9
  222. 4x8y2z12
  223. 81m4n12p12
  224. No Solution
  225. -4m-4n-3p-5
  226. x-4y-5z3
  227. -4a-3b4c6d7
  228. -9w3x6y8z-1
  229. -2p2q2r5
  230. -9x-3y4z5
  231. 24m7n5p3q-4
  232. -3x-4y-5z-3
  233. -4r3s-3t-7
  234. 6
  235. 64n6
  236. 1
  237. (x – 3y)(x2 + 3xy + 9y2)
  238. 6x2 + 13x – 5
  239. (4x – 1)(4x + 1)
  240. -6
  241. -9n
  242. -25
  243. -71
  244. x = 2
  245. 0
  246. 1
  247. x = -6
  248. 4x2 + 15x – 4
  249. 150r2s4
  250. 7
  251. 3
  252. 3
  253. 2
  254. 2a
  255. 3
  256. 35
  257. (5y – 8)(5y + 8)
  258. 4x2 – 25
  259. (4x + 5)(16x2 – 20x + 25)

Alg. II – Fund. Skills~1~NJCTL.org

Alg. II – Fund. Skills~1~NJCTL.org

Answers to Review

  1. A
  2. E
  3. C
  4. C
  5. C
  6. C
  7. D
  8. D
  9. D
  10. D
  11. C
  12. A
  13. B
  14. A
  15. B
  16. A
  17. C
  18. A
  19. A
  20. A
  21. 6
  22. 1/5
  23. x < -6
  24. b > 6
  25. 3x(x + 3)
  26. 4m2(3m – 1)
  27. 6x2(4x3 + 6x – 3)
  28. 4m2n3(4m2 – 3mn + n2)
  29. (x + 3)(x – 2)
  30. (x + 1)(3x – 2)
  31. (2x – 1)(4x + 1)
  32. (x – 5)(x + 3)
  33. (2m + 5)(m + 1)
  34. (2x + 3)(5x + 1)
  35. (x – 3)(x2 + 3x + 9)
  36. (9x – 2y)(9x + 2y)
  37. (x – 4)(2x – 3)
  38. (2m + n)(4m2 – 2mn + n2)
  39. (3b – 5)(2a – 1)
  40. (x + 4)(2y + 3)
  41. (3m – 5)(n + 4)
  42. 3xy(x – 5)(x + 2)
  43. 5m2(2m – 3)(2m + 3)
  44. x = 0, 3
  45. x = 0, -3
  46. x = -9, 2
  47. x = 2, -2
  48. m8n20
  49. x8
  50. a4b2
  51. -6x3y4
  52. 18x7y2
  53. m11
  54. x5y3
  55. 12x8
  56. 27x6y9
  57. 2xy4
  58. 16a8b12
  59. 81x4y2
  60. 81x2
  61. 2

Alg. II – Fund. Skills~1~NJCTL.org