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# Elementary and Intermediate Algebra

**by**Dugopolski, Mark

4th

### 9780073384351

0073384356

Hardcover

1/6/2011

McGraw-Hill Science/Engineering/Math

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## Related Products

## Summary

The Dugopolski series in developmental mathematics has helped thousands of students succeed in their developmental math courses. Elementary & Intermediate Algebra,4eis part of the latest offerings in the successful Dugopolski series in mathematics. In his books, students and faculty will find short, precise explanations of terms and concepts written in clear, understandable language that is mathematically accurate. Dugopolski also includes a double cross-referencing system between the examples and exercise sets, so no matter where the students start, they will see the connection between the two. Finally, the author finds it important to not only provide quality but also a wide variety and quantity of exercises and applications.

## Table of Contents

PREFACE

APPLICATIONS INDEX

1 Real Numbers and Their Properties

1.1 The Real Numbers

1.2 Fractions

1.3 Addition and Subtraction of Real Numbers

1.4 Multiplication and Division of Real Numbers

1.5 Exponential Expressions and the Order of Operations

1.6 Algebraic Expressions

1.7 Properties of the Real Numbers

1.8 Using the Properties to Simplify Expressions

Chapter 1 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 1 Test

• Critical Thinking

2 Linear Equations and Inequalities in One Variable

2.1 The Addition and Multiplication Properties of Equality

2.2 Solving General Linear Equations

2.3 More Equations

2.4 Formulas and Functions

2.5 Translating Verbal Expressions into Algebraic Expressions

2.6 Number, Geometric, and Uniform Motion Applications

2.7 Discount, Investment, and Mixture Applications

2.8 Inequalities

2.9 Solving Inequalities and Applications

Chapter 2 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 2 Test

• Making Connections: A review of Chapters 1-2

• Critical Thinking

3 Linear Equations and Inequalities in Two Variables

3.1 Graphing Lines in the Coordinate Plane

3.2 Slope

3.3 Equations of Lines in Slope-Intercept Form

3.4 The Point-Slope Form

3.5 Variations

3.6 Graphing Linear Inequalities in Two Variables

Chapter 3 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 3 Test

• Making Connections: a review of Chapters 1-3

• Critical Thinking

4 Exponents and Polynomials

4.1 The Rules of Exponents

4.2 Negative Exponents

4.3 Scientific Notation

4.4 Addition and Subtraction of Polynomials

4.5 Multiplication of Polynomials

4.6 Multiplication of Binomials

4.7 Special Products

4.8 Division of Polynomials

Chapter 4 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 4 Test

• Making Connections: a review of Chapters 1-4

• Critical Thinking

5 Factoring

5.1 Factoring Out Common Factors

5.2 Special Products and Grouping

5.3 Factoring the Trinomial ax² + bx + c with a = 1

5.4 Factoring the Trinomial ax² + bx + c with a ≠ 1

5.5 Difference and Sum of Cube and a Strategy

5.6 Solving Quadratic Equations by Factoring

Chapter 5 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 5 Test

• Making Connections: a review of Chapters 1-5

• Critical Thinking

6 Rational Expressions

6.1 Reducing Rational Expressions

6.2 Multiplication and Division

6.3 Finding the Least Common Denominator

6.4 Addition and Subtraction

6.5 Complex Fractions

6.6 Solving Equations with Rational Expressions

6.7 Applications of Ratios and Proportions

6.8 Applications of Rational Expressions

Chapter 6 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 6 Test

• Making Connections: a review of Chapters 1-6

• Critical Thinking

7 Systems of Linear Equations

7.1 The Graphing Method

7.2 The Substitution Method

7.3 The Addition Method

7.4 Systems of Linear Equations in Three Variables

Chapter 7 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 7 Test

• Making Connections: a review of Chapters 1-7

• Critical Thinking

8 More on Inequalities

8.1 Compound Inequalities in One Variable

8.2 Absolute Value Equations and Inequalities

8.3 Compound Inequalities in Two Variables

8.4 Linear Programming

Chapter 8 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 8 Test

• Making Connections: a review of Chapters 1-8

• Critical Thinking

9 Radicals and Rational Exponents

9.1 Radicals

9.2 Rational Exponents

9.3 Adding, Subtracting, and Multiplying Radicals

9.4 Quotients, Powers, and Rationalizing Denominators

9.5 Solving Equations with Radicals and Exponents

9.6 Complex Numbers

Chapter 9 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 9 Test

• Making Connections: a review of Chapters 1-9

• Critical Thinking

10 Quadratic Equations and Inequalities

10.1 Factoring and Completing the Square

10.2 The Quadratic Formula

10.3 More on Quadratic Equations

10.4 Graphing Quadratic Functions

10.5 Quadratic Inequalities

Chapter 10 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 10 Test

• Making Connections: a review of Chapters 1-10

• Critical Thinking

11 Functions

11.1 Functions and Relations

11.2 Graphs of Functions and Relations

11.3 Transformations of Graphs

11.4 Graphs of Polynomial Functions

11.5 Graphs of Rational Functions

11.6 Combining Functions

11.7 Inverse Functions

Chapter 11 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 11 Test

• Making Connections: a review of Chapters 1-11

• Critical Thinking

12 Exponential and Logarithmic Functions

12.1 Exponential Functions and Their Applications

12.2 Logarithmic Functions and Their Applications

12.3 Properties of Logarithms

12.4 Solving Equations and Applications

Chapter 12 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 12 Test

• Making Connections: a review of Chapters 1-12

• Critical Thinking

13 Nonlinear Systems and the Conic Sections

13.1 Nonlinear Systems of Equations

13.2 The Parabola

13.3 The Circle

13.4 The Ellipse and Hyperbola

13.5 Second-Degree Inequalities

Chapter 13 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 13 Test

• Making Connections: a review of Chapters 1-13

• Critical Thinking

14 Sequences and Series (Available online at www.mhhe.com/dugopolski)

14.1 Sequences

14.2 Series

14.3 Arithmetic Sequences and Series

14.4 Geometric Sequences and Series

14.5 Binomial Expansions

Chapter 14 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 14 Test

• Making Connections: A Review of Chapter 1-14

• Critical Thinking

Appendix A: Geometry Review Exercises

Appendix B: Sets

Appendix C: Chapters 1-6 Diagnostic Test

Appendix D: Chapters 1-6 Review

Answers to Selected Exercises

Index

APPLICATIONS INDEX

1 Real Numbers and Their Properties

1.1 The Real Numbers

1.2 Fractions

1.3 Addition and Subtraction of Real Numbers

1.4 Multiplication and Division of Real Numbers

1.5 Exponential Expressions and the Order of Operations

1.6 Algebraic Expressions

1.7 Properties of the Real Numbers

1.8 Using the Properties to Simplify Expressions

Chapter 1 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 1 Test

• Critical Thinking

2 Linear Equations and Inequalities in One Variable

2.1 The Addition and Multiplication Properties of Equality

2.2 Solving General Linear Equations

2.3 More Equations

2.4 Formulas and Functions

2.5 Translating Verbal Expressions into Algebraic Expressions

2.6 Number, Geometric, and Uniform Motion Applications

2.7 Discount, Investment, and Mixture Applications

2.8 Inequalities

2.9 Solving Inequalities and Applications

Chapter 2 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 2 Test

• Making Connections: A review of Chapters 1-2

• Critical Thinking

3 Linear Equations and Inequalities in Two Variables

3.1 Graphing Lines in the Coordinate Plane

3.2 Slope

3.3 Equations of Lines in Slope-Intercept Form

3.4 The Point-Slope Form

3.5 Variations

3.6 Graphing Linear Inequalities in Two Variables

Chapter 3 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 3 Test

• Making Connections: a review of Chapters 1-3

• Critical Thinking

4 Exponents and Polynomials

4.1 The Rules of Exponents

4.2 Negative Exponents

4.3 Scientific Notation

4.4 Addition and Subtraction of Polynomials

4.5 Multiplication of Polynomials

4.6 Multiplication of Binomials

4.7 Special Products

4.8 Division of Polynomials

Chapter 4 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 4 Test

• Making Connections: a review of Chapters 1-4

• Critical Thinking

5 Factoring

5.1 Factoring Out Common Factors

5.2 Special Products and Grouping

5.3 Factoring the Trinomial ax² + bx + c with a = 1

5.4 Factoring the Trinomial ax² + bx + c with a ≠ 1

5.5 Difference and Sum of Cube and a Strategy

5.6 Solving Quadratic Equations by Factoring

Chapter 5 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 5 Test

• Making Connections: a review of Chapters 1-5

• Critical Thinking

6 Rational Expressions

6.1 Reducing Rational Expressions

6.2 Multiplication and Division

6.3 Finding the Least Common Denominator

6.4 Addition and Subtraction

6.5 Complex Fractions

6.6 Solving Equations with Rational Expressions

6.7 Applications of Ratios and Proportions

6.8 Applications of Rational Expressions

Chapter 6 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 6 Test

• Making Connections: a review of Chapters 1-6

• Critical Thinking

7 Systems of Linear Equations

7.1 The Graphing Method

7.2 The Substitution Method

7.3 The Addition Method

7.4 Systems of Linear Equations in Three Variables

Chapter 7 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 7 Test

• Making Connections: a review of Chapters 1-7

• Critical Thinking

8 More on Inequalities

8.1 Compound Inequalities in One Variable

8.2 Absolute Value Equations and Inequalities

8.3 Compound Inequalities in Two Variables

8.4 Linear Programming

Chapter 8 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 8 Test

• Making Connections: a review of Chapters 1-8

• Critical Thinking

9 Radicals and Rational Exponents

9.1 Radicals

9.2 Rational Exponents

9.3 Adding, Subtracting, and Multiplying Radicals

9.4 Quotients, Powers, and Rationalizing Denominators

9.5 Solving Equations with Radicals and Exponents

9.6 Complex Numbers

Chapter 9 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 9 Test

• Making Connections: a review of Chapters 1-9

• Critical Thinking

10 Quadratic Equations and Inequalities

10.1 Factoring and Completing the Square

10.2 The Quadratic Formula

10.3 More on Quadratic Equations

10.4 Graphing Quadratic Functions

10.5 Quadratic Inequalities

Chapter 10 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 10 Test

• Making Connections: a review of Chapters 1-10

• Critical Thinking

11 Functions

11.1 Functions and Relations

11.2 Graphs of Functions and Relations

11.3 Transformations of Graphs

11.4 Graphs of Polynomial Functions

11.5 Graphs of Rational Functions

11.6 Combining Functions

11.7 Inverse Functions

Chapter 11 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 11 Test

• Making Connections: a review of Chapters 1-11

• Critical Thinking

12 Exponential and Logarithmic Functions

12.1 Exponential Functions and Their Applications

12.2 Logarithmic Functions and Their Applications

12.3 Properties of Logarithms

12.4 Solving Equations and Applications

Chapter 12 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 12 Test

• Making Connections: a review of Chapters 1-12

• Critical Thinking

13 Nonlinear Systems and the Conic Sections

13.1 Nonlinear Systems of Equations

13.2 The Parabola

13.3 The Circle

13.4 The Ellipse and Hyperbola

13.5 Second-Degree Inequalities

Chapter 13 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 13 Test

• Making Connections: a review of Chapters 1-13

• Critical Thinking

14 Sequences and Series (Available online at www.mhhe.com/dugopolski)

14.1 Sequences

14.2 Series

14.3 Arithmetic Sequences and Series

14.4 Geometric Sequences and Series

14.5 Binomial Expansions

Chapter 14 Wrap-Up

• Summary

• Enriching Your Mathematical Word Power

• Review Exercises

• Chapter 14 Test

• Making Connections: A Review of Chapter 1-14

• Critical Thinking

Appendix A: Geometry Review Exercises

Appendix B: Sets

Appendix C: Chapters 1-6 Diagnostic Test

Appendix D: Chapters 1-6 Review

Answers to Selected Exercises

Index