# Intermediate Algebra

**by**Lial, Margaret L.; Hornsby, John; McGinnis, Terry

### 9780321872180

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## Summary

**Lial Series**has helped thousands of students succeed in developmental mathematics by providing the best learning and teaching support to students and instructors.

## Author Biography

**Marge Lial** became interested in math at an early age—it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. She was particularly interested in archeology; trips to various digs and ruin sites produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan. We dedicate the new editions of the paperback developmental math series to Marge in honor of her contributions to the field in which she helped thousands of students succeed.

When **John Hornsby** enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.

A native Midwesterner,** Terry McGinnis** received her Bachelor’s of Science in Elementary Education with a concentration in Mathematics from Iowa State University. She has taught elementary and middle school mathematics, and developed and implemented the curriculum used with her students. Terry has been involved in college mathematics publishing for over 20 years, working with a variety of authors on textbooks in developmental mathematics and precalculus. After working behind the scenes on many of the Lial/Hornsby textbooks and supplements for over 10 years, Terry joined Margaret Lial and John Hornsby in 2002 as coauthor of their developmental mathematics series that includes *Introductory Algebra, Intermediate Algebra, *and *Introductory and Intermediate Algebra*. When not working, Terry enjoys spinning at a local health club, walking, and reading fiction. She is the devoted mother of two sons, Andrew and Tyler.

## Table of Contents

**R. Review of the Real Number System**

R.1 Basic Concepts

R.2 Operations on Real Numbers

R.3 Exponents, Roots, and Order of Operations

R.4 Properties of Real Numbers

**1. Linear Equations and Applications**

1.1 Linear Equations in One Variable

1.2 Formulas and Percent

1.3 Applications of Linear Equations

1.4 Further Applications of Linear Equations

**2. Linear Inequalities and Absolute Value**

2.1 Linear Inequalities in One Variable

2.2 Set Operations and Compound Inequalities

2.3 Absolute Value Equations and Inequalities

**3. Graphs, Linear Equations, and Functions**

3.1 The Rectangular Coordinate System

3.2 The Slope of a Line

3.3 Linear Equations in Two Variables

3.4 Linear Inequalities in Two Variables

3.5 Introduction to Relations and Functions

3.6 Function Notation and Linear Functions

**4. Systems of Linear Equations**

4.1 Systems of Linear Equations in Two Variables

4.2 Systems of Linear Equations in Three Variables

4.3 Applications of Linear Systems of Equations

4.4 Solving Linear Systems of Equations by Matrix Methods

**5. Exponents, Polynomials, and Polynomial Functions**

5.1 Integer Exponents and Scientific Notation

5.2 Adding and Subtracting Polynomials

5.3 Polynomial Functions

5.4 Multiplying Polynomials

5.5 Dividing Polynomials

**6. Factoring**

6.1 Greatest Common Factors; Factoring by Grouping

6.2 Factoring Trinomials

6.3 Special Factoring

6.4 A General Approach to Factoring

6.5 Solving Equations by Factoring

**7. Rational Expressions**

7.1 Rational Expressions and Functions; Multiplying and Dividing

7.2 Adding and Subtracting Rational Expressions

7.3 Complex Fractions

7.4 Equations with Rational Expressions and Graphs

7.5 Applications of Rational Expressions

7.6 Variation

**8. Roots, Radicals, and Root Functions**

8.1 Rational Expressions and Graphs

8.2 Rational Exponents

8.3 Simplifying Radical Expressions

8.4 Adding and Subtracting Radical Expressions

8.5 Multiplying and Dividing Radical Expressions

8.6 Solving Equations with Radicals

8.7 Complex Numbers

**9. Quadratic Equations, Inequalities, and Functions**

9.1 The Square Root Property and Completing the Square

9.2 The Quadratic Formula

9.3 Equations Quadratic in Form

9.4 Formulas and Applications

9.5 Graphs of Quadratic Functions

9.6 More About Parabolas and Their Applications

9.7 Polynomial and Rational Inequalities

**10. Inverse, Exponential, and Logarithmic Functions**

10.1 Composition of Functions

10.2 Inverse Functions

10.3 Exponential Functions

10.4 Logarithmic Functions

10.5 Properties of Logarithms

10.6 Common and Natural Logarithms

10.7 Exponential and Logarithmic Equations and Their Applications

**11. Nonlinear Functions, Conic Sections, and Nonlinear Systems**

11.1 Additional Graphs of Functions

11.2 The Circle and the Ellipse

11.3 The Hyperbola, and Other Functions Defined by Radicals

11.4 Nonlinear Systems of Equations

11.5 Second-Degree Inequalities and Systems of InequalitiesAppendix A: Review of Fractions

Appendix B: Solving Systems of Linear Equations by Matrix Methods

Appendix C: Synthetic Division

Answers to Selected Exercises

Solutions to Selected Exercises

Index