# Introductory Algebra

**by**Bittinger, Marvin L.

### 9780321599216

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## Summary

## Author Biography

**Marvin Bittinger**has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University Purdue University Indianapolis, and is now Professor Emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." His hobbies include hiking in Utah, baseball, golf, and bowling. In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.

## Table of Contents

**Chapter R Prealgebra Review**

R.1 Factoring and LCMs

R.2 Fraction Notation

R.3 Decimal Notation

R.4 Percent Notation

R.5 Exponential Notation and Order of Operations

R.6 Geometry

**Chapter 1 Introduction to Real Numbers and Algebraic Expressions**

1.1 Introduction to Algebra

1.2 The Real Numbers

1.3 Addition of Real Numbers

1.4 Subtraction of Real Numbers

1.5 Multiplication of Real Numbers

1.6 Division of Real Numbers

1.7 Properties of Real Numbers

1.8 Simplifying Expressions; Order of Operations

**Chapter 2 Solving Equations and Inequalities**

2.1 Solving Equations: The Addition Principle

2.2 Solving Equations: The Multiplication Principle

2.3 Using the Principles Together

2.4 Formulas

2.5 Applications of Percent

2.6 Applications and Problem Solving

2.7 Solving Inequalities

2.8 Applications and Problem Solving with Inequalities

**Chapter 3 Graphs of Linear Equations**

3.1 Graphs and Applications of Linear Equations

3.2 More with Graphing and Intercepts

3.3 Slope and Applications

3.4 Equations of Lines

3.5 Graphing Using the Slope and the *y*-intercept

3.6 Parallel and Perpendicular Lines

3.7 Graphing Inequalities in Two Variables

**Chapter 4 Polynomials: Operations**

4.1 Integers as Exponents

4.2 Exponents and Scientific Notation

4.3 Introduction to Polynomials

4.4 Addition and Subtraction of Polynomials

4.5 Multiplication of Polynomials

4.6 Special Products

4.7 Operations with Polynomials in Several Variables

4.8 Division of Polynomials

**Chapter 5 Polynomials: Factoring**

5.1 Introduction to Factoring

5.2 Factoring Trinomials of the Type* x2* +* bx* + *c*

5.3 Factoring *ax2 *+ *bx *+ *c*, *a ≠* 1:

The FOIL Method

5.4 Factoring *ax2* + *bx* + *c*, *a ≠* 1:

The *ac*-Method

5.5 Factoring Trinomial Squares and Differences of Squares

5.6 Factoring: A General Strategy

5.7 Solving Quadratic Equations by Factoring

5.8 Applications of Quadratic Equations

**Chapter 6 Rational Expressions and Equations**

6.1 Multiplying and Simplifying Rational Expressions

6.2 Division and Reciprocals

6.3 Least Common Multiples and Denominators

6.4 Adding Rational Expressions

6.5 Subtracting Rational Expressions

6.6 Solving Rational Equations

6.7 Applications Using Rational Equations and Proportions

6.8 Complex Rational Expressions

6.9 Direct and Inverse Variation

**Chapter 7 Systems of Equations**

7.1 Systems of Equations in Two Variables

7.2 The Substitution Method

7.3 The Elimination Method

7.4 Applications and Problem Solving

7.5 Applications with Motion

**Chapter 8 Radical Expressions and Equations**

8.1 Introduction to Radical Expressions

8.2 Multiplying and Simplifying with Radical Expressions

8.3 Quotients Involving Radical Expressions

8.4 Addition, Subtraction, and More Multiplication

8.5 Radical Equations

8.6 Applications with Right Triangles

**Chapter 9 Quadratic Equations**

9.1 Introduction to Quadratic Equations

9.2 Solving Quadratic Equations by Completing the Square

9.3 The Quadratic Formula

9.4 Formulas

9.5 Applications and Problem Solving

9.6 Graphs of Quadratic Equations

9.7 Functions

**Appendices**

A. Factoring Sums or Differences of Cubes

B. Finding Equations of Lines: Point-Slope Equation

C. Higher Roots

D. Sets

E. Mean, Median, and Mode