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  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Use the Language of Algebra
    4. 1.3 Add and Subtract Integers
    5. 1.4 Multiply and Divide Integers
    6. 1.5 Visualize Fractions
    7. 1.6 Add and Subtract Fractions
    8. 1.7 Decimals
    9. 1.8 The Real Numbers
    10. 1.9 Properties of Real Numbers
    11. 1.10 Systems of Measurement
    12. Key Terms
    13. Key Concepts
    14. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations and Inequalities
    1. Introduction
    2. 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 2.2 Solve Equations using the Division and Multiplication Properties of Equality
    4. 2.3 Solve Equations with Variables and Constants on Both Sides
    5. 2.4 Use a General Strategy to Solve Linear Equations
    6. 2.5 Solve Equations with Fractions or Decimals
    7. 2.6 Solve a Formula for a Specific Variable
    8. 2.7 Solve Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Math Models
    1. Introduction
    2. 3.1 Use a Problem-Solving Strategy
    3. 3.2 Solve Percent Applications
    4. 3.3 Solve Mixture Applications
    5. 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
    6. 3.5 Solve Uniform Motion Applications
    7. 3.6 Solve Applications with Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Graphs
    1. Introduction
    2. 4.1 Use the Rectangular Coordinate System
    3. 4.2 Graph Linear Equations in Two Variables
    4. 4.3 Graph with Intercepts
    5. 4.4 Understand Slope of a Line
    6. 4.5 Use the Slope-Intercept Form of an Equation of a Line
    7. 4.6 Find the Equation of a Line
    8. 4.7 Graphs of Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Systems of Linear Equations
    1. Introduction
    2. 5.1 Solve Systems of Equations by Graphing
    3. 5.2 Solving Systems of Equations by Substitution
    4. 5.3 Solve Systems of Equations by Elimination
    5. 5.4 Solve Applications with Systems of Equations
    6. 5.5 Solve Mixture Applications with Systems of Equations
    7. 5.6 Graphing Systems of Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Polynomials
    1. Introduction
    2. 6.1 Add and Subtract Polynomials
    3. 6.2 Use Multiplication Properties of Exponents
    4. 6.3 Multiply Polynomials
    5. 6.4 Special Products
    6. 6.5 Divide Monomials
    7. 6.6 Divide Polynomials
    8. 6.7 Integer Exponents and Scientific Notation
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Factoring
    1. Introduction
    2. 7.1 Greatest Common Factor and Factor by Grouping
    3. 7.2 Factor Trinomials of the Form x2+bx+c
    4. 7.3 Factor Trinomials of the Form ax2+bx+c
    5. 7.4 Factor Special Products
    6. 7.5 General Strategy for Factoring Polynomials
    7. 7.6 Quadratic Equations
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Rational Expressions and Equations
    1. Introduction
    2. 8.1 Simplify Rational Expressions
    3. 8.2 Multiply and Divide Rational Expressions
    4. 8.3 Add and Subtract Rational Expressions with a Common Denominator
    5. 8.4 Add and Subtract Rational Expressions with Unlike Denominators
    6. 8.5 Simplify Complex Rational Expressions
    7. 8.6 Solve Rational Equations
    8. 8.7 Solve Proportion and Similar Figure Applications
    9. 8.8 Solve Uniform Motion and Work Applications
    10. 8.9 Use Direct and Inverse Variation
    11. Key Terms
    12. Key Concepts
    13. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Roots and Radicals
    1. Introduction
    2. 9.1 Simplify and Use Square Roots
    3. 9.2 Simplify Square Roots
    4. 9.3 Add and Subtract Square Roots
    5. 9.4 Multiply Square Roots
    6. 9.5 Divide Square Roots
    7. 9.6 Solve Equations with Square Roots
    8. 9.7 Higher Roots
    9. 9.8 Rational Exponents
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Quadratic Equations
    1. Introduction
    2. 10.1 Solve Quadratic Equations Using the Square Root Property
    3. 10.2 Solve Quadratic Equations by Completing the Square
    4. 10.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 10.4 Solve Applications Modeled by Quadratic Equations
    6. 10.5 Graphing Quadratic Equations in Two Variables
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
  13. Index

Be Prepared

9.1

8181 8181 8181

9.2

3.853.85

9.3

100100 100100.

9.4

511511

9.5

n6n6

9.6

1q81q8

9.7

12x12x 5m+5n5m+5n

9.8

5x2x5x2x

9.9

24uv24uv

9.10

7242n7242n

9.11

8+2a+a28+2a+a2

9.12

30483048

9.13

55

9.14

499x2499x2

9.15

33 8181

9.16

2222

9.17

n=2orn=4n=2orn=4

9.18

y9y9

9.19

n12n12

9.20

x5x5

9.21

53605360

9.22

64x6y1564x6y15

9.23

11251125

Try It

9.1

−7−7 1515

9.2

88 −11−11

9.3

not a real number −9−9

9.4

−7−7 not a real number

9.5

7 5

9.6

17 2323

9.7

6<38<76<38<7

9.8

9<84<109<84<10

9.9

3.323.32

9.10

3.613.61

9.11

y4y4 z6z6

9.12

m2m2 b5b5

9.13

8x8x

9.14

13y13y

9.15

−11y−11y

9.16

−10p−10p

9.17

10ab10ab

9.18

15mn15mn

9.19

7x157x15

9.20

9w189w18

9.21

13x5y713x5y7

9.22

12p6q1012p6q10

9.23

4343

9.24

3535

9.25

122122

9.26

123123

9.27

b2bb2b

9.28

p4pp4p

9.29

4x3x4x3x

9.30

7v4v7v4v

9.31

4y22y4y22y

9.32

5a43a5a43a

9.33

7a3b22ab7a3b22ab

9.34

6m4n55mn6m4n55mn

9.35

5+535+53

9.36

2+722+72

9.37

2323

9.38

2525

9.39

5454

9.40

7979

9.41

5454

9.42

7979

9.43

aa

9.44

x2x2

9.45

5x25x2

9.46

6z6z

9.47

197197

9.48

279279

9.49

2p6p72p6p7

9.50

2x23x52x23x5

9.51

4m5mn34m5mn3

9.52

3u36uv43u36uv4

9.53

8x238x23

9.54

2a252a25

9.55

5yx65yx6

9.56

4m35n35n4m35n35n

9.57

22

9.58

−43−43

9.59

9x9x

9.60

8u8u

9.61

7p6q7p6q

9.62

6a3b6a3b

9.63

911911

9.64

11101110

9.65

5+265+26

9.66

−57+25−57+25

9.67

−27x−27x

9.68

3y3y

9.69

−25xy−25xy

9.70

00

9.71

9292

9.72

7373

9.73

22

9.74

55

9.75

6363

9.76

−155−155

9.77

33

9.78

00

9.79

1415214152

9.80

11251125

9.81

m32mm32m

9.82

p3pp3p

9.83

20x212x320x212x3

9.84

28y324y228y324y2

9.85

10x310x3

9.86

−5x2−5x2

9.87

3232 362362

9.88

5252 902902

9.89

12151215

9.90

272272

9.91

3x223x22 10y2y10y2y

9.92

2x332x33 6y2y6y2y

9.93

144x310144x310

9.94

144y25y144y25y

9.95

12 1515

9.96

16 20

9.97

330 200

9.98

210 96

9.99

625625 23362336

9.100

12+6612+66 7+727+72

9.101

18+618+6 6+1226+122

9.102

−40+42−40+42 27+14327+143

9.103

−3+26−3+26

9.104

−2+210−2+210

9.105

−66+157−66+157

9.106

411411411411

9.107

1+9211+921

9.108

−12203−12203

9.109

12+8m15m12+8m15m

9.110

1047n15n1047n15n

9.111

102+202102+202 55+6655+66

9.112

4112541125 12136101213610

9.113

4+20m+25m4+20m+25m

9.114

924n+16n924n+16n

9.115

11

9.116

−4−4

9.117

−11−11

9.118

−159−159

9.119

2222

9.120

3333

9.121

41054105

9.122

234234

9.123

2323

9.124

4343

9.125

r2r2

9.126

p27p27

9.127

5s85s8

9.128

5q265q26

9.129

9x2y29x2y2

9.130

10n3m10n3m

9.131

533533

9.132

655655

9.133

5252

9.134

334334

9.135

146146

9.136

6868

9.137

1313

9.138

5555

9.139

2(23)12(23)1

9.140

5(53)225(53)22

9.141

3(1+5)43(1+5)4

9.142

4+654+65

9.143

5(x2)x25(x2)x2

9.144

10(y+3)y310(y+3)y3

9.145

(p+2)p22(p+2)p22

9.146

(q10)q102(q10)q102

9.147

no yesyes

9.148

no yesyes

9.149

1010

9.150

77

9.151

233233

9.152

310310

9.153

1313

9.154

3535

9.155

no solutionno solution

9.156

no solutionno solution

9.157

2,32,3

9.158

5,65,6

9.159

77

9.160

33

9.161

12721272

9.162

31133113

9.163

no solution

9.164

no solution

9.165

no solutionno solution

9.166

no solutionno solution

9.167

no solutionno solution

9.168

no solutionno solution

9.169

19.2feet19.2feet

9.170

52.0cm52.0cm

9.171

9seconds9seconds

9.172

3.5seconds3.5seconds

9.173

42.7miles per hour42.7miles per hour

9.174

54.1miles per hour54.1miles per hour

9.175

3 4 3

9.176

10 2 2

9.177

−5−5 not real −2−2

9.178

−6−6 not real −4−4

9.179

|b||b| ww |m||m| qq

9.180

|y||y| pp |z||z| qq

9.181

u3u3 v5v5

9.182

c4c4 d4d4

9.183

3x93x9 3|q7|3|q7|

9.184

5p35p3 3q53q5

9.185

|y|y24|y|y24 zz23zz23

9.186

pp35pp35 q2q6q2q6

9.187

343343 244244

9.188

553553 394394

9.189

3p32p33p32p3 2q24q242q24q24

9.190

4m32m234m32m23 3|n|2n343|n|2n34

9.191

−343−343 not realnot real

9.192

−553−553 not realnot real

9.193

|x||x| y3y3

9.194

m2m2 n2n2

9.195

26632663 3|m|2m243|m|2m24

9.196

−4−4 3|n|243|n|24

9.197

3c34c3d23c34c3d2 2x2|y|5x2y42x2|y|5x2y4

9.198

2r5s32r5s3 3m32m24|n3|3m32m24|n3|

9.199

23x523x5 293293

9.200

210y4210y4 23262326

9.201

3333 624624

9.202

2323 525525

9.203

2y4y23+3y24y232y4y23+3y24y23 3r23r34+4r23r243r23r34+4r23r24

9.204

2z25z3+3z5z32z25z3+3z5z3 2|s3|5s4+4|s|5s242|s3|5s4+4|s|5s24

9.205

tt m3m3 r4r4

9.206

bb z3z3 p4p4

9.207

s12s12 x13x13 b14b14

9.208

v12v12 p13p13 p14p14

9.209

(10m)12(10m)12 (3n)15(3n)15 (486y)14(486y)14

9.210

(3k)17(3k)17 (5j)14(5j)14 (1024a)13(1024a)13

9.211

6 2 2

9.212

10 3 3

9.213

−5−5 −5−5 1515

9.214

−2−2 −2−2 1212

9.215

not real −8−8 1818

9.216

not real −4−4 1414

9.217

x52x52 z34z34 y25y25

9.218

a25a25 b73b73 m54m54

9.219

8 9 125

9.220

32 729 8

9.221

132132 17291729 1818

9.222

1818 1919 11251125

9.223

−64−64 164164 not a real number

9.224

−729−729 17291729 not a real number

9.225

9 y3y3 m

9.226

25 z n

9.227

p2p2 q6q6 x8x8

9.228

r10r10 s9s9 m2m2

9.229

u v15v15 1x1x

9.230

c2c2 1m1m 1d1d

9.231

8x158x15 4y294y29

9.232

64m1264m12 729n35729n35

9.233

m2m2 n3n3

9.234

u3u3 v5v5

Section 9.1 Exercises

1.

6

3.

8

5.

3

7.

10

9.

−2−2

11.

−1−1

13.

not a real number

15.

not a real number

17.

5

19.

7

21.

8<70<98<70<9

23.

14<200<1514<200<15

25.

4.36

27.

7.28

29.

yy

31.

a7a7

33.

7x7x

35.

11m1011m10

37.

9x189x18

39.

−9x9−9x9

41.

−8a−8a

43.

12xy12xy

45.

13w4y513w4y5

47.

3c4d63c4d6

49.

25 centimeters

51.

Answers will vary.

Section 9.2 Exercises

53.

3333

55.

5555

57.

102102

59.

152152

61.

202202

63.

153153

65.

x3xx3x

67.

pppp

69.

m6mm6m

71.

r12rr12r

73.

7n8n7n8n

75.

9r7r9r7r

77.

7m22m7m22m

79.

5r65r5r65r

81.

10p62p10p62p

83.

11m112m11m112m

85.

7m3n53mn7m3n53mn

87.

5r6s43rs5r6s43rs

89.

10p4q53pq10p4q53pq

91.

11m6n102mn11m6n102mn

93.

5+235+23

95.

1+351+35

97.

5656

99.

1+101+10

101.

7878

103.

114114

105.

6767

107.

3535

109.

x2x2

111.

1y21y2

113.

10x210x2

115.

4p44p4

117.

635635

119.

259259

121.

4x36x114x36x11

123.

5m23m45m23m4

125.

7r22r107r22r10

127.

2q37152q3715

129.

5r43rs45r43rs4

131.

2p37pq2p37pq

133.

5x35x3

135.

11pp911pp9

137.

4xy34xy3

139.

12pqp12pqp

141.

17.0feet17.0feet 12.0feet12.0feet

143.

Answers will vary.

Section 9.3 Exercises

145.

3232

147.

9595

149.

77

151.

9y9y

153.

−3a−3a

155.

7c7c

157.

8a2b8a2b

159.

5m+n5m+n

161.

137137

163.

−311−311

165.

−53+75−53+75

167.

82358235

169.

42a42a

171.

3c3c

173.

43ab43ab

175.

pqpq

177.

9292

179.

55

181.

−23−23

183.

7373

185.

−82−82

187.

163163

189.

5252

191.

55

193.

33

195.

1112211122

197.

a22aa22a

199.

2c35c2c35c

201.

36p2542p2236p2542p22

203.

10r42+12r4610r42+12r46

205.

14x514x5

207.

4y24y2

209.

6262

211.

2k272k27

213.

2323

215.

22

217.

1313

219.

a25aa25a

221.

19191919

223.

5353

225.

33

227.

8x68x6

229.

124.5inches124.5inches

231.

Answers will vary.

Section 9.4 Exercises

233.

44 186186

235.

7272 160

237.

303303

239.

−186−186

241.

−302−302

243.

282282

245.

5y235y23 6n2n6n2n

247.

8y328y32 11s3s11s3s

249.

40b2340b23

251.

144d4144d4

253.

54y4y54y4y

255.

−96k5k−96k5k

257.

11 21

259.

23 3

261.

−234 180

263.

10521052 56

265.

2441124411 52265226

267.

−14711−14711 67726772

269.

44+81144+811 1515

271.

18521852 21732173

273.

60+2360+23

275.

52+3252+32

277.

27972797

279.

−62+555−62+555

281.

41+75541+755

283.

−81+4478−81+4478

285.

18+7ww18+7ww

287.

66+73n+15n66+73n+15n

289.

27+81127+811 2912529125

291.

351010351010 82+48282+482

293.

97

295.

39

297.

−127−127

299.

33

301.

−243−243

303.

−2103−2103

305.

7y357y35

307.

2929

309.

2971729717

311.

4.6feet4.6feet 21sq. feet21sq. feet

313.

31.9squareyards31.9squareyards

315.

when squaring a negative, it becomes a positive since the negative is not included in the parenthesis, it is not squared, and remains negative

Section 9.5 Exercises

317.

3232

319.

223223

321.

12241224

323.

2+522+52

325.

4545

327.

4343

329.

2x22x2 10m2710m27

331.

5r65r6

333.

3p10217q23p10217q2

335.

8n3m38n3m3

337.

2222

339.

1+531+53

341.

4545

343.

y313y313

345.

563563

347.

677677

349.

3131331313

351.

103103

353.

45454545

355.

332332

357.

15101510

359.

70207020

361.

1333513335

363.

3(311)−23(311)−2 −2(1+5)−2(1+5)

365.

5(56)195(56)19 3(3+7)3(3+7)

367.

3(m+5)m53(m+5)m5

369.

2(x+6)x62(x+6)x6

371.

(r+5)r52(r+5)r52

373.

5y2x5y2x

375.

3535

377.

239239

379.

3(55)203(55)20

381.

2(x+3)x32(x+3)x3

383.

(x+22)x82(x+22)x82

385.

5104seconds5104seconds

387.

Answers will vary.

Section 9.6 Exercises

389.

yesyes nono

391.

no yes

393.

3

395.

14

397.

14

399.

1717

401.

135135

403.

5252

405.

no solutionno solution

407.

no solutionno solution

409.

10,1110,11 55

411.

8,98,9 1111

413.

33

415.

55

417.

not a real number

419.

1414

421.

no solutionno solution 57165716

423.

no solutionno solution 6

425.

no solution

427.

36

429.

15

431.

11.4feet11.4feet

433.

8seconds8seconds

435.

15.8seconds15.8seconds

437.

72miles per hour72miles per hour

439.

53.0miles per hour53.0miles per hour

441.

Answers will vary.

Section 9.7 Exercises

443.

33 22 33

445.

55 66 44

447.

−4−4 not realnot real −3−3

449.

−8−8 not a real number −1−1

451.

aa |b||b|

453.

|k||k| |p||p|

455.

a2a2 b9b9

457.

r2r2 s10s10

459.

−2c3−2c3 5d55d5

461.

2r22r2 3s63s6

463.

uu25uu25 vv56vv56

465.

pp35pp35 q2q23q2q23

467.

553553 226226

469.

554554 333333

471.

2a3a252a3a25 5b3b35b3b3

473.

8pp238pp23 3q4q343q4q34

475.

−325−325 not realnot real

477.

−2−2 not realnot real

479.

dd |m||m|

481.

r3r3 |c3||c3|

483.

−5−5 2mm242mm24

485.

363363 2|r|2r342|r|2r34

487.

2r23rs352r23rs35 2u2uv362u2uv36

489.

5u35u3v5u35u3v 3c59c4d23c59c4d2

491.

215q3215q3 −4274−4274

493.

.

.
495.

223223 −234−234

497.

334+524334+524 13231323

499.

2b10b23+3b1032b10b23+3b103 2v210v2445v342v210v2445v34

501.

22

503.

|b||b|

505.

5d55d5

507.

s2s24s2s24

509.

2y3y242y3y24

511.

not realnot real

513.

2x2x52x2x5

515.

2u2uv362u2uv36

517.

224224

519.

3u6u34+43u343u6u34+43u34

521.

55

523.

Answers may vary.

Section 9.8 Exercises

525.

rr s3s3 t4t4

527.

g7g7 h5h5 j25j25

529.

r18r18 s110s110 t14t14

531.

u15u15 v12v12 w116w116

533.

(5x)14(5x)14 (9y)18(9y)18 7(3z)157(3z)15

535.

(25a)13(25a)13 (3b)12(3b)12 (40c)110(40c)110

537.

5 3 2

539.

6 2 3

541.

−3−3 −3−3 1313

543.

−10−10 −10−10 110110

545.

not a real number −7−7 1717

547.

not a real number 11 −1−1

549.

−2−2 1313
−5−5

551.

r74r74 s35s35 t73t73

553.

a13a13 b52b52 c53c53

555.

100 125 8

557.

64 3125 256

559.

32,768 17291729 181181

561.

1000 116,807116,807 not a real number

563.

−512−512
15121512 not a real number

565.

−343−343 13431343 not a real number

567.

216 nn q3q3

569.

100 x2x2 y4y4

571.

a2a2 b9b9
cc

573.

h8h8 k9k9 j14j14

575.

ss z2z2 1w1w

577.

uu rr 1n1n

579.

3r153r15 2s1142s114

581.

9m129m12 125n2125n2

583.

r2sr2s u3v4u3v4

585.

r8s5r8s5 u8v4u8v4

587.

a3a3 b4b4

589.

mm n2n2

591.

nn

593.

b6b6

595.

1z21z2

597.

2s1102s110

599.

u2v3u2v3

601.

15.6 feet

603.

8 seconds

605.

Answers will vary.

Review Exercises

607.

12

609.

−9−9

611.

not a real number

613.

17

615.

12<155<1312<155<13

617.

7.55

619.

8b8b

621.

15mn15mn

623.

7y7y

625.

11cd11cd

627.

7272

629.

y9yy9y

631.

6n6n6n6n

633.

5n36n5n36n

635.

6r2s3rs6r2s3rs

637.

1+21+2

639.

3232

641.

y2y2

643.

6q26q2

645.

26132613

647.

3r2r23r2r2

649.

2rs3r52rs3r5

651.

125125

653.

4m4m

655.

1113+231113+23

657.

33rs5rs33rs5rs

659.

5252

661.

9393

663.

00

665.

17n2217n22

667.

247247

669.

180y2180y2

671.

8

673.

50

675.

2010720107

677.

13221322

679.

513x6x513x6x

681.

1+12p+36p1+12p+36p

683.

−19−19

685.

3232

687.

4343

689.

y210y210

691.

21532153

693.

5353

695.

21142114

697.

16123−1116123−11

699.

−845−845

701.

2p6p32p6p3

703.

5

705.

7272

707.

4 and 5

709.

13

711.

432432

713.

0

715.

116116

717.

11

719.

7.5 seconds

721.

2 4

723.

dd |v||v|

725.

2x22x2 2y22y2

727.

dd

.
729.

2c2c352c2c35 2d3d342d3d34

731.

−543−543 not a real number

733.

w3w3w3w3

735.

3z23z2

737.

22052205

739.

224224

741.

2t3t35+32t452t3t35+32t45

743.
.
745.

v16v16

747.

(10z)16(10z)16

749.

2

751.

1515

753.

1616

755.

n85n85

757.

32,768

759.

159,049159,049

761.

x8x8

763.

2s9162s916

765.

z2z2

Practice Test

767.

13m2|n|13m2|n|

769.

413+52413+52

771.

60y2360y23

773.

14q+4q14q+4q

775.

3x33x3 2y32y3

777.

y2y2

779.

00

781.

343

783.

1w1w

785.

6464

787.

42

789.

6.1 seconds

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