# Algebra for College Students

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

### 9780321715401

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## Summary

## Author Biography

**Marge Lial** was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is affiliated with American River College. Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have 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.

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), and has been an avid 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 both 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

**Chapter 1: Review of the Real Number System**

1.1 Basic Concepts

1.2 Operations on Real Numbers

1.3 Exponents, Roots, and Order of Operations

1.4 Properties of Real Numbers

*Study Skills: Reading Your Math Textbook*

** **

**Chapter 2: Linear Equations, Inequalities, and Applications**

2.1 Linear Equations in One Variable

*Study Skills: Tackling Your Homework*

2.2 Formulas and Percent

2.3 Applications of Linear Equations

*Study Skills: Taking Lecture Notes*

2.4 Further Applications of Linear Equations

*Summary Exercises on Solving Applied Problems *

2.5 Linear Inequalities in One Variable

*Study Skills: Using Study Cards*

2.6 Set Operations and Compound Inequalities

*Study Skills: Using Study Cards Revisited*

2.7 Absolute Value Equations and Inequalities

*Summary Exercises on Solving Linear and Absolute Value Equations and Inequalities *

*Study Skills: Reviewing a Chapter*

** **

**Chapter 3: Graphs, Linear Equations, and Functions**

3.1 The Rectangular Coordinate System

*Study Skills: Managing Your Time*

3.2 The Slope of a Line

3.3 Linear Equations in Two Variables

*Summary Exercises on Slopes and Equations of Lines *

3.4 Linear Inequalities in Two Variables

3.5 Introduction to Relations and Functions

3.6 Function Notation and Linear Functions

*Study Skills: Taking Math Tests*

**Chapter 4: Systems of Linear Equations**

4.1 Systems of Linear Equations in Two Variables

*Study Skills: Analyzing Your Test Results*

4.2 Systems of Linear Equations in Three Variables

4.3 Applications of Systems of Linear Equations

4.4 Solving Systems of Linear Equations by Matrix Methods

**Chapter 5: Exponents, Polynomials, and Polynomial Functions **

5.1 Integer Exponents and Scientific Notation

5.2 Adding and Subtracting Polynomials

5.3 Polynomial Functions, Graphs, and Composition

5.4 Multiplying Polynomials

5.5 Dividing Polynomials

**Chapter 6: Factoring**

6.1 Greatest Common Factors and Factoring by Grouping

6.2 Factoring Trinomials

6.3 Special Factoring

6.4 A General Approach to Factoring

6.5 Solving Equations by Factoring

** **

**Chapter 7: Rational Expressions and Functions**

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

*Summary Exercises on Rational Expressions and Equations*

7.5 Applications of Rational Expressions

7.6 Variation

**Chapter 8: Roots, Radicals, and Root Functions**

8.1 Radical 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

*Summary Exercises on Operations with Radicals and Rational Exponents*

8.6 Solving Equations with Radicals

8.7 Complex Numbers

*Study Skills: Preparing for Your Math Final Exam*

**Chapter 9: Quadratic Equations and Inequalities**

9.1 The Square Root Property and Completing the Square

9.2 The Quadratic Formula

9.3 Equations Quadratic in Form

*Summary Exercises on Solving Quadratic Equations*

9.4 Formulas and Further Applications

9.5 Polynomial and Rational Inequalities

**Chapter 10: Additional Graphs of Functions and Relations**

10.1 Review of Operations and Composition

10.2 Graphs of Quadratic Functions

10.3 More About Parabolas and Their Applications

10.4 Symmetry; Increasing and Decreasing Functions

10.5 Piecewise Linear Functions

**Chapter 11: Inverse, Exponential, and Logarithmic Functions**

11.1 Inverse Functions

11.2 Exponential Functions

11.3 Logarithmic Functions

11.4 Properties of Logarithms

11.5 Common and Natural Logarithms

11.6 Exponential and Logarithmic Equations; Further Applications

**Chapter 12: Polynomial and Rational Functions**

12.1 Zeros of Polynomial Functions (I)

12.2 Zeros of Polynomial Functions (II)

12.3 Graphs and Applications of Polynomial Functions

*Summary Exercises on Polynomial Functions and Graphs*

12.4 Graphs and Applications of Rational Functions

**Chapter 13: Conic Sections and Nonlinear Systems**

13.1 The Circle and the Ellipse

13.2 The Hyperbola and Functions Defined by Radicals

13.3 Nonlinear Systems of Equations

13.4 Second-Degree Inequalities, Systems of Inequalities, and Linear Programming

** **

**Chapter 14: Further Topics in Algebra**

14.1 Sequences and Series

14.2 Arithmetic Sequences

14.3 Geometric Sequences

14.4 The Binomial Theorem

14.5 Mathematical Induction

14.6 Counting Theory

14.7 Basics of Probability

**Appendixes **

Appendix A Properties of Matrices

Appendix B Matrix Inverses

Appendix C Determinants and Cramer’s Rule