Practice Workbook Answers (continued)

Practice Workbook Answersc. x 2 17x 30 0d. x 2 3x 28 0(continued)4. a. x 121c. x 555. a. (x 2)Ax 2 2x 4Bb. (x 2)Ax 2 2x 4Bc. (5x 2)A25x 2 10x 4Bd. (5x 2)A25x 2 10x 4Be. (x 6)Ax 2 12Bf. (2x 5)A4x 2 12x 21Bg. (x 2)3h. (4x 3)Ax 2 x 1Bi. (y (2x 1))(y (2x 1))Ay 2 (2x 1)2 Bj. Ax 2 (y 2)BAx 2 (y 2)Bk. A(y 2) zBAAy 2B 2 z(y 2) z 2Bl. (x 1)3b. x 123d. x 35. a. x 2b. x 2 2x 4c. x 2 4d. x 4 2x 3 4x 2 8x 16e. Ax 2 2x 4B Ax 2 2x 4Bf. x 4 166 1 4x 3 1 16g. x(x 12)(x 2 2)h.(x 2 1 2)(x 4 2 2x 1 4)(x 4 1 2x 1 4)(x 1 2)(x 2 2)136. g(x) 2x3x 1 2 ; the graphs of f (x) andg(x) are identical, except for a hole9 R in the graphdiscontinuity at Q 3, 11of f (x).6. a. x 2b. x 2 4x 4c. x 3 6x 2 12x 8d. x 4 8x 3 24x 2 32x 16e. x 5 10x 4 40x 3 80x 2 80x 327. A 1; B 1Chapter 3Lessons 3.2 and 3.3Additional PracticeLessons 2.14 and 2.15Additional Practice1. a. nonec. nonee. noneAx 2 5BAx 2 7B1. a.b. Ax 3 4B 2c. Ax 2 2BAx 4 2x2 4Bd. Ax 3 x 2 xB 2e. AAx 2 6) xB AAx 2 6B xBf. Ax 3 a 3B 2 a 3x 3g. (x 2)Ax 2 2x 4B(x 2)Ax 2 2x 4Bh. Ax 4 8BAx 4 8B2. I. a. x 6, 1c. nonee. none2. a. Ax A 4 "21BBAx A 4 "21BBb. 2Ax A 1 "5BBAx A 1 "5BB3. a–c. Answers may vary. Samples:a. x 2 6x 4 0b. x 2 6x 4 0c. x 4 16x 2 4 0b. x 1, 6d. x 4f. x 1b. noned. x 4f. noneII. a. nonec. nonee. noneb. noned. nonef. x 217III. a. noneb. nonec. x 27 42"73d. nonee. x 4"3f. noneIV. a–f. There are no nonrealsolutions.CME Project Algebra 2 Teaching Resources Pearson Education, Inc. All rights reserved.159

Practice Workbook Answers(continued)3. a. Yes; it simplifies to 10.b. No; it simplifies to 24 10 "21.c. Yes; it simplifies to 1.d. Yes; it simplifies to 26.7. a. 1c. 1 4ie. 49 20ig. 11 24ib. 1d. 1 4if. 49 20ih. 11 24i4. a. 412 5 i8. a. 131356b. 23365 65 ib. 3e. 5 3 "25c. 8d. 8f. 6 "265. a. 12 7 "21c. 22 20 "21c.b. 8 39 "21d. 14 0 "21x 2 1 2xyi 2 y 2x2 1 y2Lessons 3.7 and 3.8Additional Practice6. a. (x 3)Ax 2 3x 9Bb. x 3, 23 4 23"231. a–d.c. "21d. x 2 4y 2e. 45f. "214i 5 3ib. "217. a. 272i 4Lessons 3.4 and 3.5Additional Practice1. a. 12. a. x 6 ic. x {5ib. i 224 2i 5 3ic. ib. x 12 id. z 2 { 3i5 3i 4i2. a–d.3. z 4 5i96i4. a. any complex number where b 0b. None exists; all rational numbersare real.c. any fraction with an integernumerator and denominatord. any complex number where a isrational and with b 0e. None exists; all real numbers arecomplex, where b 0.(3 i)484i72i60i48i36i(3 i )324i5. Solve x 2 4 0 to get x 4"24,which simplifies to x {2i. Therefore,by factoring, x 2 4 (x 2i)(x 2i).6. a. 3 3i5 3i12i3 ib. 4 9ic. 14 22id. 25 15 i3 2ie. 13134 5if. 4141(3 i )26CME Project Algebra 2 Teaching Resources Pearson Education, Inc. All rights reserved.16012182430

Practice Workbook Answers(continued)c. x 2 i or x 2 i3. a–b.z z4ix yi2iz z 42 2ix yi 4ic. Answers may vary. Sample:z, z, z z, and the origin form aparallelogram.d. Answers may vary. Sample:z, z, z z, and the origin form aparallelogram.d. x 2 2i or x 2 2i4i2i4. a. x 3 or x 1 4 42 2i2i 4i2445. 2ii 4i ib. x 22462 i 2i 3i4i2i 4 24i 24 26. a. "172c. "4424 2i6 3ib. "26d. 10"107. 3 2i, 5, 6 i, 4 5i 4iCME Project Algebra 2 Teaching Resources Pearson Education, Inc. All rights reserved.161

Practice Workbook Answers8. a.(continued)d.wzw6iwz 2i4i46810 4i2izwz 2i46810zw 10 5i12e. 6zw 13 6i 4 2zb.zw14i 4i12i 6i w10i 8i8i 10iw6i 12izwzw 6 12if.2i 4 2zzw 3 14ic.w4 2izzw46zwzw 56i4iLesson 3.9 Additional Practicew1. a. "41; 38.7 2zc. "41; 141.3 4b. "41; 321.3 d. "41; 218.7 2. a. u z u 2 "5; arg z 63.43 ;zw 1 7ib. u z u 2 "5; arg z 296.57 ;c. u z u 2 "5; arg z 116.57 ;d. u z u 2 "5; arg z 243.43 ;CME Project Algebra 2 Teaching Resources Pearson Education, Inc. All rights reserved.162

Practice Workbook Answers3. a.b.c.d.u z 2 u 20; arg z 2 126.86 u z 2 u 20; arg z 2 233.14 u z 2 u 20; arg z 2 233.14 u z 2 u 20; arg z 2 126.86 (continued)c.2ii1z 24. a–b. 12 iz2i1z 2i 22 2i1 2 "3 iz77zd.5. The magnitude doubles and thedirection rotates 90 counterclockwise.1z123 i6. a. 0 b. 18.43 c. 36.86 d. 53.13 e. 71.57 7. a.zic. 2; 315 1 3 1iz1010i8. a. u z u "10; u w u "17;1zu zw u "170b. u z u "10; u w u 2"5; 11u zw u 10"2c. u z u 4; u w u 5; u zw u 20 izd. u z u "10; u w u "410 ;u zw u 104 2.51 1 1iz22b.Lesson 3.11 Additional Practice2i1. a. 16; 120 b. 64; 180 c. x 2 4x 16 01z 22. IV1z3. a. For z, take the square root of themagnitude and half the directionof z 2; for z 3, cube the magnitudeand triple the direction of z; for z n,raise the magnitude of z to the nthpower, and multiply the directionof z by n. 2i1 2 1iz55CME Project Algebra 2 Teaching Resources Pearson Education, Inc. All rights reserved.163

Practice Workbook Answers4. a. No, the magnitude is 9.(continued)d.b. No, the magnitude could be anynumber from 0 to 6.4i 1 3ic. Yes, the magnitude is 3.2id. No, the magnitude is 13 .2e. No, the magnitude is 9.4i4 3i 2Lessons 3.12 and 3.13Additional Practice4 2i3 2i1. a. "10, 18.4 ; 2"5, 26.6 4ib.b. 10"2, 45 c. 10, 36.8 ; 20, 53.2 4i2. a. ( 3 i)3 4( 3 i)2 2( 3 i) 20 0b. 3 i, 2c.2 i 444i 2 3i 4i2i3 4i 4c.65 i6. 3"5 2"5 30; 63 333 396 1 2i 44 2if. No, the magnitude is 6.5. a.6 4i2 2i5 10i10i 2 4i8i3. a. 1b. 3ic. 1 2id. 3 4i4i 4 3i4. x 3 4x 2 10x 40 0 4 22 2i465. 20 sides8 iCME Project Algebra 2 Teaching Resources Pearson Education, Inc. All rights reserved.1644

Practice Workbook Answersb. n 126. a. 1, 30 c.5. a. 2z 2w 32y 2w 12y 2z 0i 1(continued)b. 2z 2w 1 2y 2w 32y 2z 01c. y 12 , z 12 , w 1d. x 0, y 12 , z 12 , w 1 i6. a 2, b 1, c 37. There is no solution to the system.The equations represent two linesthat are parallel and therefore neverintersect.7. a. The magnitude of each solutionis 1. The directions goingcounterclockwise are 60 , 120 ,180 , 240 , 300 , and 360 .b. {1, {i, { a 12 1 "23 b , { a 12 2 "23 bLesson 4.3 Additional Practice1. a8.i221 22 28 x ba b a b2 21 27 y332. a22 1026 x ba b a b26 y30213x21 3 11 y 21 3. 5 226 22 22 16z211182161x224. 1 23 22 3 216 y 2 7510z4 i5. 7, 3, and 11Chapter 46. 2x 3y 6z 5x 3y z 06x 2y z 2Lesson 4.2 Additional Practice1. x 2, y 02117. 332. x 2, y 2, z 33. x 0, y 0, z 04. x 1, y 4, z 2, w 3CME Project Algebra 2 Teaching Resources Pearson Education, Inc. All rights reserved.165

solutions. Practice Workbook Answers (continued) . Practice Workbook Answers (continued) CME Project Algebra 2 Teaching Resources . 180 , 240 , 300 , and 360 . b. {1, {i, {a1 2 1 "3 2 b, {a 1 2 2 "3 2 b 8. Chapter 4 Lesson 4.2 Additional Practice 1. x 2, y 0 2. x 2, y 2, z 3 3. x 0, y 0, z 0 4.