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  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Use the Language of Algebra
    3. 1.2 Integers
    4. 1.3 Fractions
    5. 1.4 Decimals
    6. 1.5 Properties of Real Numbers
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations
    1. Introduction
    2. 2.1 Use a General Strategy to Solve Linear Equations
    3. 2.2 Use a Problem Solving Strategy
    4. 2.3 Solve a Formula for a Specific Variable
    5. 2.4 Solve Mixture and Uniform Motion Applications
    6. 2.5 Solve Linear Inequalities
    7. 2.6 Solve Compound Inequalities
    8. 2.7 Solve Absolute Value Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Graphs and Functions
    1. Introduction
    2. 3.1 Graph Linear Equations in Two Variables
    3. 3.2 Slope of a Line
    4. 3.3 Find the Equation of a Line
    5. 3.4 Graph Linear Inequalities in Two Variables
    6. 3.5 Relations and Functions
    7. 3.6 Graphs of Functions
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Systems of Linear Equations
    1. Introduction
    2. 4.1 Solve Systems of Linear Equations with Two Variables
    3. 4.2 Solve Applications with Systems of Equations
    4. 4.3 Solve Mixture Applications with Systems of Equations
    5. 4.4 Solve Systems of Equations with Three Variables
    6. 4.5 Solve Systems of Equations Using Matrices
    7. 4.6 Solve Systems of Equations Using Determinants
    8. 4.7 Graphing Systems of Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Polynomials and Polynomial Functions
    1. Introduction
    2. 5.1 Add and Subtract Polynomials
    3. 5.2 Properties of Exponents and Scientific Notation
    4. 5.3 Multiply Polynomials
    5. 5.4 Dividing Polynomials
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Factoring
    1. Introduction to Factoring
    2. 6.1 Greatest Common Factor and Factor by Grouping
    3. 6.2 Factor Trinomials
    4. 6.3 Factor Special Products
    5. 6.4 General Strategy for Factoring Polynomials
    6. 6.5 Polynomial Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Rational Expressions and Functions
    1. Introduction
    2. 7.1 Multiply and Divide Rational Expressions
    3. 7.2 Add and Subtract Rational Expressions
    4. 7.3 Simplify Complex Rational Expressions
    5. 7.4 Solve Rational Equations
    6. 7.5 Solve Applications with Rational Equations
    7. 7.6 Solve Rational Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Roots and Radicals
    1. Introduction
    2. 8.1 Simplify Expressions with Roots
    3. 8.2 Simplify Radical Expressions
    4. 8.3 Simplify Rational Exponents
    5. 8.4 Add, Subtract, and Multiply Radical Expressions
    6. 8.5 Divide Radical Expressions
    7. 8.6 Solve Radical Equations
    8. 8.7 Use Radicals in Functions
    9. 8.8 Use the Complex Number System
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Quadratic Equations and Functions
    1. Introduction
    2. 9.1 Solve Quadratic Equations Using the Square Root Property
    3. 9.2 Solve Quadratic Equations by Completing the Square
    4. 9.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 9.4 Solve Quadratic Equations in Quadratic Form
    6. 9.5 Solve Applications of Quadratic Equations
    7. 9.6 Graph Quadratic Functions Using Properties
    8. 9.7 Graph Quadratic Functions Using Transformations
    9. 9.8 Solve Quadratic Inequalities
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Exponential and Logarithmic Functions
    1. Introduction
    2. 10.1 Finding Composite and Inverse Functions
    3. 10.2 Evaluate and Graph Exponential Functions
    4. 10.3 Evaluate and Graph Logarithmic Functions
    5. 10.4 Use the Properties of Logarithms
    6. 10.5 Solve Exponential and Logarithmic Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Conics
    1. Introduction
    2. 11.1 Distance and Midpoint Formulas; Circles
    3. 11.2 Parabolas
    4. 11.3 Ellipses
    5. 11.4 Hyperbolas
    6. 11.5 Solve Systems of Nonlinear Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  13. 12 Sequences, Series and Binomial Theorem
    1. Introduction
    2. 12.1 Sequences
    3. 12.2 Arithmetic Sequences
    4. 12.3 Geometric Sequences and Series
    5. 12.4 Binomial Theorem
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  14. 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
    11. Chapter 11
    12. Chapter 12
  15. Index

Be Prepared

12.1

5, 7, 9, 11

12.2

−1,1,−1,1−1,1,−1,1

12.3

20

12.4

3, 7, 11, 15

12.5

(5,2)(5,2)

12.6

654

12.7

3434

12.8

81; 116116

12.9

12; 36; 108

12.10

35

12.11

9x2+30x+259x2+30x+25

12.12

x22xy+y2x22xy+y2

Try It

12.1

−1,2,5,8,11−1,2,5,8,11

12.2

−3,−1,1,3,5−3,−1,1,3,5

12.3

7,13,31,85,2477,13,31,85,247

12.4

−3,−1,3,11,27−3,−1,3,11,27

12.5

−1,4,−9,16,−25−1,4,−9,16,−25

12.6

1,−8,27,−64,1251,−8,27,−64,125

12.7

an=3nan=3n

12.8

an=5nan=5n

12.9

an=(−1)n3nan=(−1)n3n

12.10

an=(−1)n+1n2an=(−1)n+1n2

12.11

an=12nan=12n

12.12

an=1n2an=1n2

12.13

2,1,13,112,1602,1,13,112,160

12.14

3,32,12,18,1403,32,12,18,140

12.15

12,16,112,120,13012,16,112,120,130

12.16

12,13,14,15,1612,13,14,15,16

12.17

45

12.18

60

12.19

163163

12.20

8

12.21

n=1512nn=1512n

12.22

n=151n2n=151n2

12.23

n=15(−1)n+1n2n=15(−1)n+1n2

12.24

n=15(−1)n2nn=15(−1)n2n

12.25

The sequence is arithmetic with common difference d=11d=11. The sequence is arithmetic with common difference d=−6d=−6.
The sequence is not arithmetic as all the differences between the consecutive terms are not the same.

12.26

The sequence is not arithmetic as all the differences between the consecutive terms are not the same. The sequence is arithmetic with common difference d=2.d=2.
The sequence is arithmetic with common difference d=−5.d=−5.

12.27

7,3,−1,−5,−9,7,3,−1,−5,−9,

12.28

11,3,−5,−13,−21,11,3,−5,−13,−21,

12.29

241

12.30

−106−106

12.31

a11=2.a11=2. The general term is an=−3n+35.an=−3n+35.

12.32

a19=−55.a19=−55. The general term is an=−4n+21.an=−4n+21.

12.33

a1=5,a1=5,d=4.d=4. The general term is an=4n+1.an=4n+1.

12.34

a1=8,a1=8,d=−3.d=−3. The general term is an=−3n+11.an=−3n+11.

12.35

1,890

12.36

1,515

12.37

2,300

12.38

5,250

12.39

2,670

12.40

3,045

12.41

The sequence is geometric with common ratio r=3.r=3. The sequence is geometric with common ratio r=14.r=14. The sequence is not geometric. There is no common ratio.

12.42

The sequence is not geometric. There is no common ratio. The sequence is geometric with common ratio r=2.r=2. The sequence is geometric with common ratio r=12.r=12.

12.43

7,−21,63,−189,5677,−21,63,−189,567

12.44

6,−24,96,−384,15366,−24,96,−384,1536

12.45

16,56116,561

12.46

116,384116,384

12.47

a9=39,366.a9=39,366. The general term is an=6(3)n1.an=6(3)n1.

12.48

a11=7,168.a11=7,168. The general term is an=7(2)n1.an=7(2)n1.

12.49

3,145,7253,145,725

12.50

10,460,353,20010,460,353,200

12.51

393,204393,204

12.52

10,23010,230

12.53

96

12.54

25632563

12.55

4949

12.56

8989

12.57

$10,000$10,000

12.58

$3,333.33$3,333.33

12.59

$88,868.36$88,868.36

12.60

$698,201.57$698,201.57

12.61

x5+5x4y+10x3y2+10x2y3x5+5x4y+10x3y2+10x2y3
+5xy4+y5+5xy4+y5

12.62

p7+7p6q+21p5q2+35p4q3p7+7p6q+21p5q2+35p4q3
+35p3q4+21p2q5+7pq6+q7+35p3q4+21p2q5+7pq6+q7

12.63

x4+8x3+24x2+32x+16x4+8x3+24x2+32x+16

12.64

x6+6x5+15x4+20x3+15x2x6+6x5+15x4+20x3+15x2
+6x+1+6x+1

12.65

16x496x3+216x2216x+8116x496x3+216x2216x+81

12.66

64x6192x5+240x4160x364x6192x5+240x4160x3
+60x212x+1+60x212x+1

12.67

6 1 1 35

12.68

2 1 1 6

12.69

x5+5x4y+10x3y2+10x2y3x5+5x4y+10x3y2+10x2y3
+5xy4+y5+5xy4+y5

12.70

m6+6m5n+15m4n2+20m3n3m6+6m5n+15m4n2+20m3n3
+15m2n4+6mn5+n6+15m2n4+6mn5+n6

12.71

x515x4+90x3270x2x515x4+90x3270x2
+405x243+405x243

12.72

y66y5+15y420y3+15y2y66y5+15y420y3+15y2
6y+16y+1

12.73

243x5810x4y+1080x3y2243x5810x4y+1080x3y2
720x2y3+240xy432y5720x2y3+240xy432y5

12.74

256x4768x3y+864x2y2256x4768x3y+864x2y2
432xy3+81y4432xy3+81y4

12.75

15x4y215x4y2

12.76

70a4b470a4b4

12.77

3,584

12.78

280

Section 12.1 Exercises

1.

−5,−3,−1,1,3−5,−3,−1,1,3

3.

4,7,10,13,164,7,10,13,16

5.

5,7,11,19,355,7,11,19,35

7.

1,5,21,73,2331,5,21,73,233

9.

2,1,89,1,32252,1,89,1,3225

11.

1,32,54,78,9161,32,54,78,916

13.

−2,4,−6,8,−10−2,4,−6,8,−10

15.

1,−4,9,−16,251,−4,9,−16,25

17.

1,14,19,116,1251,14,19,116,125

19.

an=8nan=8n

21.

an=n+5an=n+5

23.

an=en+2an=en+2

25.

an=(−1)n5nan=(−1)n5n

27.

an=(−1)nn3an=(−1)nn3

29.

an=(−1)n2nan=(−1)n2n

31.

an=14nan=14n

33.

an=nn+1an=nn+1

35.

an=52nan=52n

37.

4,2,23,16,1304,2,23,16,130

39.

3,6,18,72,3603,6,18,72,360

41.

2,24,720,40320,36288002,24,720,40320,3628800

43.

1,12,13,14,151,12,13,14,15

45.

1,12,23,32,2451,12,23,32,245

47.

2,32,83,152,14452,32,83,152,1445

49.

1+4+9+16+25=551+4+9+16+25=55

51.

5+7+9+11+13+15=605+7+9+11+13+15=60

53.

2+4+8+16=302+4+8+16=30

55.

41+41+42+46=323=102341+41+42+46=323=1023

57.

2+6+12+20+30=702+6+12+20+30=70

59.

12+23+34+45+56=712012+23+34+45+56=7120

61.

n=1513nn=1513n

63.

n=151n3n=151n3

65.

n=152nn=152n

67.

n=15(−1)n+13nn=15(−1)n+13n

69.

n=110(−1)n2nn=110(−1)n2n

71.

n=17(2n+12)n=17(2n+12)

73.

Answers will vary.

75.

Answers will vary.

Section 12.2 Exercises

77.

The sequence is arithmetic with common difference d=8.d=8.

79.

The sequence is not arithmetic.

81.

The sequence is arithmetic with common difference d=−3.d=−3.

83.

11,18,25,32,3911,18,25,32,39

85.

−7,−3,1,5,9−7,−3,1,5,9

87.

14,5,−4,−13,−2214,5,−4,−13,−22

89.

163163

91.

131131

93.

−79−79

95.

a20=−34.a20=−34. The general term is an=−2n+6.an=−2n+6.

97.

a11=59.a11=59. The general term is an=5n+4.an=5n+4.

99.

a8=−13.a8=−13. The general term is an=−5n+27.an=−5n+27.

101.

a1=11,a1=11,d=3.d=3. The general term is an=3n+8.an=3n+8.

103.

a1=21,a1=21,d=−8.d=−8. The general term is an=−8n+29.an=−8n+29.

105.

a1=−15,a1=−15,d=3.d=3. The general term is an=3n18.an=3n18.

107.

1,635

109.

−1,065−1,065

111.

360

113.

6,325

115.

–3,575

117.

6,280

119.

4,125

121.

−3,850−3,850

123.

Answers will vary.

125.

Answers will vary.

Section 12.3 Exercises

127.

The sequence is geometric with common ratio r=4.r=4.

129.

The sequence is geometric with common ratio r=12.r=12.

131.

The sequence is geometric with a common ratio r=−2.r=−2.

133.

The sequence is geometric with common ratio r=12.r=12.

135.

The sequence is arithmetic with common difference d=5.d=5.

137.

The sequence is geometric with common ratio r=12.r=12.

139.

4,12,36,108,3244,12,36,108,324

141.

−4,8,−16,32,−64−4,8,−16,32,−64

143.

27,9,3,1,1327,9,3,1,13

145.

472,392472,392

147.

3,072

149.

0.00010.0001

151.

a9=2,304.a9=2,304. The general term is an=9(2)n1.an=9(2)n1.

153.

a15=219,683.a15=219,683. The general term is an=−486(13)n1.an=−486(13)n1.

155.

a10=0.000000001.a10=0.000000001. The general term is an=(0.1)n1.an=(0.1)n1.

157.

57,395,62457,395,624

159.

−65,538−65,538

161.

7,174,45359,049121.57,174,45359,049121.5

163.

65,53465,534

165.

40884088

167.

29,52465614.529,52465614.5

169.

3232

171.

9292

173.

no sum as r1r1

175.

2,048

177.

1313

179.

7979

181.

511511

183.

$6666.67$6666.67 $4000$4000 $15,000$15,000 $7500$7500

185.

$295,581.88$295,581.88

187.

$14,234.10$14,234.10

189.

Answers will vary.

191.

Answers will vary.

Section 12.4 Exercises

193.

a8+8a7b+28a6b2+56a5b3a8+8a7b+28a6b2+56a5b3
+70a4b4+56a3b5+28a2b6+70a4b4+56a3b5+28a2b6
+8ab7+b8+8ab7+b8

195.

p9+9p8q+36p7q2+84p6q3p9+9p8q+36p7q2+84p6q3
+126p5q4+126p4q5+84p3q6+126p5q4+126p4q5+84p3q6
+36p2q7+9pq8+q9+36p2q7+9pq8+q9

197.

a66a5b+15a4b220a3b3a66a5b+15a4b220a3b3
+15a2b46ab5+b6+15a2b46ab5+b6

199.

x3+15x2+75x+125x3+15x2+75x+125

201.

y7+7y6+21y5+35y4+35y3y7+7y6+21y5+35y4+35y3
+21y2+7y+1+21y2+7y+1

203.

z612z5+60z4160z3+240z2z612z5+60z4160z3+240z2
192z+64192z+64

205.

243x5405x4+270x390x2243x5405x4+270x390x2
+15x1+15x1

207.

27x3135x2+225x12527x3135x2+225x125

209.

27x3+135x2y+225xy2+125y327x3+135x2y+225xy2+125y3

211.

7 1 1 45

213.

4 1 1 55

215.

m5+5m4n+10m3n2+10m2n3m5+5m4n+10m3n2+10m2n3
+5mn4+n5+5mn4+n5

217.

s7+7s6t+21s5t2+35s4t3s7+7s6t+21s5t2+35s4t3
+35s3t4+21s2t5+7st6+t7+35s3t4+21s2t5+7st6+t7

219.

y412y3+54y2108y+81y412y3+54y2108y+81

221.

q312q2+48q64q312q2+48q64

223.

625x41000x3y+600x2y2625x41000x3y+600x2y2
160xy3+16y4160xy3+16y4

225.

243x5+1620x4y+4320x3y2243x5+1620x4y+4320x3y2
+5760x2y3+3840xy4+1024y5+5760x2y3+3840xy4+1024y5

227.

126a5b4126a5b4

229.

462x5y6462x5y6

231.

112

233.

324

235.

30,618

237.

Answers will vary.

239.

Answers will vary.

Review Exercises

241.

7,13,31,85,2477,13,31,85,247

243.

34,516,764,9256,11102434,516,764,9256,111024

245.

an=9nan=9n

247.

an=en4an=en4

249.

an=nn+2an=nn+2

251.

16,112,120,130,14216,112,120,130,142

253.

−3+(−1)+1+3+5−3+(−1)+1+3+5
+7+9=21+7+9=21

255.

4+4+2+23+16=6564+4+2+23+16=656

257.

n=15(−1)n13nn=15(−1)n13n

259.

n=154nn=154n

261.

The sequence is arithmetic with common difference d=6.d=6.

263.

5,8,11,14,175,8,11,14,17

265.

−13,−7,−1,5,11−13,−7,−1,5,11

267.

−129−129

269.

a18=103.a18=103. The general term is an=7n23.an=7n23.

271.

a1=1,a1=1,d=4.d=4. The general term is an=4n3.an=4n3.

273.

−1,095−1,095

275.

585585

277.

4,8504,850

279.

980980

281.

The sequence is not geometric.

283.

The sequence is geometric with common ratio r=−2.r=−2.

285.

128,32,8,2,12128,32,8,2,12

287.

1,5361,536

289.

a12=−25,165,824.a12=−25,165,824. The general term is an=6(−4)n1.an=6(−4)n1.

291.

−43,692

293.

3906.253906.25

295.

1898=23.6251898=23.625

297.

343657.167343657.167

299.

411411

301.

$1,634,421.27$1,634,421.27

303.

x44x3y+6x2y24xy3+y4x44x3y+6x2y24xy3+y4

305.

32y5240y4+720y31080y232y5240y4+720y31080y2
+810y243+810y243

307.

11 1 1 56

309.

1 1 1 55

311.

t99t8+36t784t6+126t5t99t8+36t784t6+126t5
126t4+84t336t2+9t1126t4+84t336t2+9t1

313.

256x4+768x3y+864x2y2256x4+768x3y+864x2y2
+432xy3+81y4+432xy3+81y4

315.

84a3b684a3b6

317.

135

319.

280

Practice Test

321.

14,15,16,17,1814,15,16,17,18

323.

−4+1664+256=204−4+1664+256=204

325.

−13,−10,−7,−4,−1−13,−10,−7,−4,−1

327.

a23=59.a23=59. The general term is an=3n10.an=3n10.

329.

1,3251,325

331.

3,2603,260

333.

The sequence is geometric with common ratio r=13.r=13.

335.

5,242,8805,242,880

337.

797,162797,162

339.

5656

341.

$1,409,344.19$1,409,344.19

343.

8 1 1 210

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© Apr 15, 2020 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License 4.0 license. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.