Intermediate Algebra

Tom Carson’s first teaching experience was teaching guitar while an undergraduate student studying electrical engineering. That experience helped him to realize that his true gift and passion are for teaching. He earned his MAT in mathematics at the University of South Carolina. In addition to teaching at Midlands Technical College, Columbia State Community College, and Franklin Classical School, Tom has served on the faculty council and has been a board member of the South Carolina Association of Developmental Educators (SCADE). Ever the teacher, Tom teaches outside the classroom by presenting at conferences such as NADE, AMATYC, and ICTCM on topics such as Combating Innumeracy, Writing in Mathematics, and Implementing a Study System. In addition to his work on the Carson Developmental Algebra Series, Tom also is the author of Prealgebra, Fourth Edition.   Bill Jordan received his BS from Rollins College and his MAT from Tulane University. A decorated teacher for more than 40 years, Bill has served as the chair of the math department at Seminole Community College and has taught at Rollins College. He has been a member and leader of numerous professional organizations, including the Florida Two-Year College Mathematical Association (president), Florida Council of Teachers of Mathematics (district director), and others. In addition to his work on the Carson series, Bill is also the lead author of Integrated Algebra and Arithmetic, 2/e, also published by Pearson. In his spare time, he enjoys fishing, traveling, and hiking.

Preface vi

To the Student xiii

Learning Styles Inventory xv

The Carson Math Study System xvii

 

1 Real Numbers and

Expressions 1

 

1.1 Sets and the Structure of Algebra 2

1.2 Operations with Real Numbers; Properties

of Real Numbers 12

1.3 Exponents, Roots, and Order of

Operations 24

1.4 Evaluating and Rewriting Expressions 34

Summary and Review Exercises 45

Practice Test 53

 

2 Linear Equations and Inequalities

in One Variable 55

 

2.1 Linear Equations and Formulas 56

2.2 Solving Problems 66

2.3 Solving Linear Inequalities 74

2.4 Compound Inequalities 85

2.5 Equations Involving Absolute Value 96

2.6 Inequalities Involving Absolute

Value 100

Summary and Review Exercises 108

Practice Test 116

Chapters 1—2 Cumulative Review

Exercises 118

 

3 Equations and Inequalities in Two

Variables; Functions 120

 

3.1 Graphing Linear Equations 121

3.2 The Slope of a Line 133

3.3 The Equation of a Line 145

3.4 Graphing Linear Inequalities 156

3.5 Introduction to Functions and Function

Notation 164

Summary and Review Exercises 182

Practice Test 192

Chapters 1—3 Cumulative Review

Exercises 194

 

4 Systems of Linear Equations

and Inequalities 197

 

4.1 Solving Systems of Linear Equations

in Two Variables 198

4.2 Solving Systems of Linear Equations

in Three Variables 216

4.3 Solving Applications Using Systems

of Equations 223

4.4 Solving Systems of Linear Equations

Using Matrices 236

4.5 Solving Systems of Linear Inequalities 245

Summary and Review Exercises 252

Practice Test 259

Chapters 1—4 Cumulative Review

Exercises 261

 

5 Exponents, Polynomials, and

Polynomial Functions 263

5.1 Exponents and Scientific Notation 264

5.2 Polynomials and Polynomial Functions 280

5.3 Multiplying Polynomials 294

5.4 Dividing Polynomials 305

5.5 Synthetic Division and the Remainder

Theorem 313

Summary and Review Exercises 319

Practice Test 327

Chapters 1—5 Cumulative Review

Exercises 329

 

6 Factoring 331

6.1 Greatest Common Factor and

Factoring by Grouping 332

6.2 Factoring Trinomials 340

6.3 Factoring Special Products

and Factoring Strategies 350

6.4 Solving Equations by Factoring 361

Summary and Review Exercises 374

Practice Test 381

Chapters 1—6 Cumulative Review

Exercises 383

 

7 Rational Expressions and

Equations 386

7.1 Simplifying, Multiplying, and Dividing

Rational Expressions 387

7.2 Adding and Subtracting Rational

Expressions 402

7.3 Simplifying Complex Rational

Expressions 414

7.4 Solving Equations Containing Rational

Expressions 423

7.5 Applications with Rational Expressions;

Variation 430

Summary and Review Exercises 444

Practice Test 456

Chapters 1—7 Cumulative Review

Exercises 458

 

8 Rational Exponents, Radicals,

and Complex Numbers 460

 

8.1 Radical Expressions and Functions 461

8.2 Rational Exponents 471

8.3 Multiplying, Dividing, and Simplifying

Radicals 481

8.4 Adding, Subtracting, and Multiplying

Radical Expressions 489

8.5 Rationalizing Numerators and Denominators

of Radical Expressions 496

8.6 Radical Equations and Problem Solving 506

8.7 Complex Numbers 515

Summary and Review Exercises 523

Practice Test 533

Chapters 1—8 Cumulative Review

Exercises 535

 

9 Quadratic Equations and

Functions 537

 

9.1 The Square Root Principle and Completing

the Square 538

9.2 Solving Quadratic Equations Using the

Quadratic Formula 548

9.3 Solving Equations That Are Quadratic

in Form 559

9.4 Graphing Quadratic Functions 568

9.5 Solving Nonlinear Inequalities 580

Summary and Review Exercises 591

Practice Test 598

Chapters 1—9 Cumulative Review

Exercises 601

 

10 Exponential and Logarithmic

Functions 603

 

10.1 Composite and Inverse Functions 604

10.2 Exponential Functions 616

10.3 Logarithmic Functions 625

10.4 Properties of Logarithms 633

10.5 Common and Natural Logarithms 641

10.6 Exponential and Logarithmic Equations with

Applications 646

Summary and Review Exercises 657

Practice Test 669

Chapters 1—10 Cumulative Review

Exercises 671

 

11 Conic Sections 673

 

11.1 Parabolas and Circles 674

11.2 Ellipses and Hyperbolas 687

11.3 Nonlinear Systems of Equations 698

11.4 Nonlinear Inequalities and Systems of

Inequalities 704

Summary and Review Exercises 711

Practice Test 720

Chapters 1—11 Cumulative Review

Exercises 722

Appendixes 673

 

A. Arithmetic Sequences and Series APP-1

B. Geometric Sequences and Series APP-8

C. The Binomial Theorem APP-15

D. Solving Systems of Linear Equations

Using Cramer’s Rule APP-20

E. Permutations and Combinations

(available online via MyMathLab)

F. Probability

(available online via MyMathLab)

 

Photo Credits P-1

Collaborative Exercises C-1

Answers A-1

Glossary G-1

Index of Applications IA-1

Index I-1