# Intermediate Algebra

## 3rd Edition

**Authors:**Charles P. McKeague

**eBook ISBN:**9781483218748

**Imprint:**Academic Press

**Published Date:**1st January 1986

**Page Count:**582

## Description

Intermediate Algebra, Third Edition focuses on operations, principles, and approaches involved in intermediate algebra.

The manuscript first ponders on basic properties and definitions, linear equations and inequalities in one variable, and exponents and polynomials. Discussions focus on factoring trinomials, special factoring, solving equations by factoring, linear equations in one variable, equations with absolute value, simple and compound inequalities, and addition and subtraction of real numbers. The text then ponders on rational expressions, rational exponents and roots, and quadratic equations. Topics include additional items involving solutions to equations, quadratic inequalities, completing the square, simplified form for radicals, addition and subtraction of radical expressions, basic properties and reducing to lowest terms, multiplication and division of rational expressions, and division of polynomials. The book takes a look at sequences and series, logarithms, relations and functions, and conic sections, including ellipses and hyperbolas, nonlinear systems, inverse of a function, relations and functions, and series and summation notation.

The publication is a dependable reference for students and researchers interested in intermediate algebra.

## Table of Contents

Preface to the Instructor

Preface to the Student

1 Basic Properties and Definitions

1.1 Basic Definitions

1.2 The Real Numbers, Opposites, Reciprocals, and Absolute Value

1.3 Simple and Compound Inequalities

1.4 Properties of Real Numbers

1.5 Addition and Subtraction of Real Numbers

1.6 Multiplication and Division of Real Numbers

Summary and Review

Chapter Test

2 Linear Equations and Inequalities in One Variable

2.1 Linear Equations in One Variable

2.2 Linear Inequalities in One Variable

2.3 Equations with Absolute Value

2.4 Inequalities Involving Absolute Value

2.5 Formulas

2.6 Word Problems

Summary and Review

Chapter Test

3 Exponents and Polynomials

3.1 Properties of Exponents I

3.2 Properties of Exponents II

3.3 Polynomials, Sums, and Differences

3.4 Multiplication of Polynomials

3.5 The Greatest Common Factor and Factoring by Grouping

3.6 Factoring Trinomials

3.7 Special Factoring

3.8 Factoring: A General Review

3.9 Solving Equations by Factoring

Summary and Review

Chapter Test

4 Rational Expressions

4.1 Basic Properties and Reducing to Lowest Terms

4.2 Division of Polynomials

4.3 Multiplication and Division of Rational Expressions

4.4 Addition and Subtraction of Rational Expressions

4.5 Complex Fractions

4.6 Equations Involving Rational Expressions

4.7 Word Problems

Summary and Review

Chapter Test

5 Rational Exponents and Roots

5.1 Rational Exponents

5.2 More Expressions Involving Rational Exponents

5.3 Simplified Form for Radicals

5.4 Addition and Subtraction of Radical Expressions

5.5 Multiplication and Division of Radical Expressions

5.6 Equations with Radicals

5.7 Complex Numbers

Summary and Review

Chapter Test

6 Quadratic Equations

6.1 Completing the Square

6.2 The Quadratic Formula

6.3 Additional Items Involving Solutions to Equations

6.4 Equations Quadratic in Form

6.5 Quadratic Inequalities

Summary and Review

Chapter Test

7 Linear Equations and Inequalities

7.1 Graphing in Two Dimensions

7.2 The Slope of a Line

7.3 The Equation of a Straight Line

7.4 Linear Inequalities in Two Variables

7.5 Variation

Summary and Review

Chapter Test

8 Systems of Linear Equations

8.1 Systems of Linear Equations in Two Variables

8.2 Systems of Linear Equations in Three Variables

8.3 Introduction to Determinants

8.4 Cramer's Rule

8.5 Word Problems

Summary and Review

Chapter Test

9 The Conic Sections

9.1 Graphing Parabolas

9.2 The Circle

9.3 Ellipses and Hyperbolas

9.4 Second-Degree Inequalities

9.5 Nonlinear Systems

Summary and Review

Chapter Test

10 Relations and Functions

10.1 Relations and Functions

10.2 Function Notation

10.3 Classification of Functions

10.4 The Inverse of a Function

Summary and Review

Chapter Test

11 Logarithms

11.1 Logarithms are Exponents

11.2 Properties of Logarithms

11.3 Common Logarithms and Natural Logarithms

11.4 Exponential Equations and Change of Base

Summary and Review

Chapter Test

12 Sequences and Series

12.1 Sequences

12.2 Series and Summation Notation

12.3 Arithmetic Progressions

12.4 Geometric Progressions

12.5 The Binomial Expansion

Summary and Review

Chapter Test

Appendix A: Synthetic Division

Appendix B: Using a Calculator

Appendix C: Matrix Solutions to Systems of Equations

Appendix D: Powers, Roots, and Prime Factors

Appendix E: Common Logarithms

Answers to Odd-Numbered Problems and Chapter Tests

Index

## Details

- No. of pages:
- 582

- Language:
- English

- Copyright:
- © Academic Press 1986

- Published:
- 1st January 1986

- Imprint:
- Academic Press

- eBook ISBN:
- 9781483218748