# Elementary & Intermediate Algebra

**by**Woodbury, George

### 9780321665485

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## Summary

## Author Biography

**George Woodbury**earned his bachelor’s degree in mathematics from the University of California—Santa Barbara in 1990 and his master’s degree in mathematics from California State University—Northridge in 1994. He currently teaches at College of the Sequoias in Visalia, CA, just outside of Fresno. He has been honored as an instructor by both his students and his colleagues. Aside from teaching and writing, George served as the department chair of the math/engineering division from 1999 through 2004.

## Table of Contents

**1. Review of Real Numbers**

1.1. Integers, Opposites, and Absolute Values

1.2. Operations with Integers

1.3. Fractions

1.4. Operations with Fractions

1.5. Decimals and Percents

1.6. Basic Statistics

1.7. Exponents and Order of Operations

1.8 Introduction to Algebra

**2. Linear Equations**

2.1. Introduction to Linear Equations

2.2. Solving Linear Equations: A General Strategy

2.3. Problem Solving; Applications of Linear Equations

2.4. Applications Involving Percentages; Ration and Proportion

2.5. Linear Inequalities

**3. Graphing Linear Equations**

3.1. The Rectangular Coordinate System; Equations in Two Variables

3.2. Graphing Linear Equations and Their Intercepts

3.3. Slope of a Line

3.4. Linear Functions

3.5. Parallel and Perpendicular Lines

3.6. Equations of Lines

3.7. Linear Inequalities

**4. Systems of Equations**

4.1. Systems of Linear Equations; Solving Systems by Graphing

4.2. Solving Systems of Equations by Using the Substitution Method

4.3. Solving Systems of Equations by Using the Addition Method

4.4. Applications of Systems of Equations

4.5. Systems of Linear Inequalities

**5. Exponents and Polynomials**

5.1. Exponents

5.2. Negative Exponents; Scientific Notation

5.3. Polynomials; Addition and Subtraction of Polynomials

5.4. Multiplying Polynomials

5.5. Dividing of Polynomials

**6. Factoring and Quadratic Equations**

6.1. An Introduction to Factoring; the Greatest Common Factor; Factoring by Grouping

6.2. Factoring Trinomials of the Form *x* ^{2} + *bx* + *c*

6.3. Factoring Trinomials of the Form *ax* ^{2} + *bx* + *c*, where *a* ≠ 1

6.4. Factoring Special Binomials

6.5. Factoring Polynomials: A General Strategy

6.6. Solving Quadratic Equations by Factoring

6.7. Quadratic Functions

6.8. Applications of Quadratic Equations and Quadratic Functions

**7. Rational Expressions and Equations**

7.1. Rational Expressions and Functions

7.2. Multiplication and Division of Rational Expressions

7.3. Addition and Subtraction of Rational Expressions That Have the Same Denominator

7.4. Addition and Subtraction of Rational Expressions That Have Different Denominators

7.5. Complex Fractions

7.6. Rational Equations

7.7. Applications of Rational Equations

**8. A Transition**

8.1. Linear Equations and Absolute Value Equations

8.2. Linear Inequalities and Absolute Value Inequalities

8.3. Graphing Linear Equations and Functions; Graphing Absolute Value Functions

8.4. Review of Factoring; Quadratic Equations and Rational Equations

8.5. Systems of Equations (Two Equations in Two Unknowns, Three Equations in Three Unknowns)

**9. Radical Expressions and Equations**

9.1. Square Roots; Radical Notation

9.2. Rational Exponents

9.3. Simplifying, Adding, and Subtracting Radical Expressions

9.4. Multiplying and Dividing Radical Expressions

9.5. Radical Equations and Applications of Radical Equations

9.6. The Complex Numbers

**10. Quadratic Equations**

10.1. Solving Quadratic Equations by Extracting Square Roots; Completing the Square

10.2. The Quadratic Formula

10.3. Equations That Are Quadratic in Form

10.4. Graphing Quadratic Equations

10.5. Applications Using Quadratic Equations

10.6. Quadratic and Rational Inequalities

**11. Functions**

11.1. Review of Functions

11.2. Linear Functions

11.3. Quadratic Functions

11.4. Other Functions and Their Graphs

11.5. The Algebra of Functions

11.6. Inverse Functions

**12. Logarithmic and Exponential Functions**

12.1. Exponential Functions

12.2. Logarithmic Functions

12.3. Properties of Logarithms

12.4. Exponential and Logarithmic Equations

12.5. Applications of Exponential and Logarithmic Functions

12.6. Graphing Exponential and Logarithmic Functions

**13. Conic Sections**

13.1. Parabolas

13.2. Circles

13.3. Ellipses

13.4. Hyperbolas

13.5. Nonlinear Systems of Equations

**14. Sequences, Series, and the Binomial Theorem**

14.1. Sequences and Series

14.2. Arithmetic Sequences and Series

14.3. Geometric Sequences and Series

14.4. The Binomial Theorem

**Appendices**

A-1. Synthetic Division

A-2. Using Matrices to Solve Systems of Equations