## Table of Contents

**1. Introduction to Algebraic Expressions**

1.1 Introduction to Algebra

1.2 The Commutative, Associative, and Distributive Laws

1.3 Fraction Notation

1.4 Positive and Negative Real Numbers

1.5 Addition of Real Numbers

1.6 Subtraction of Real Numbers

1.7 Multiplication and Division of Real Numbers

1.8 Exponential Notation and Order of Operations

**2. Equations, Inequalities, and Problem Solving**

2.1 Solving Equations

2.2 Using the Principles Together

2.3 Formulas

2.4 Applications with Percent

2.5 Problem Solving

2.6 Solving Inequalities

2.7 Solving Applications with Inequalities

**3. Introduction to Graphing**

3.1 Reading Graphs, Plotting Points, and Scaling Graphs

3.2 Graphing Linear Equations

3.3 Graphing and Intercepts

3.4 Rates

3.5 Slope

3.6 Slope-Intercept Form

3.7 Point—Slope Form and Equations of Lines

**4. Polynomials**

4.1 Exponents and Their Properties

4.2 Negative Exponents and Scientific Notation

4.3 Polynomials

4.4 Addition and Subtraction of Polynomials

4.5 Multiplication of Polynomials

4.6 Special Products

4.7 Polynomials in Several Variables

4.8 Division of Polynomials

**5. Polynomials and Factoring**

5.1 Introduction to Factoring

5.2 Factoring Trinomials of the Type *x*^{2}+*bx*+*c*

5.3 Factoring Trinomials of the Type *ax*^{2}+*bx*+*c*

5.4 Factoring Perfect-Square Trinomials and Differences of Squares

5.5 Factoring Sums or Differences of Cubes

5.6 Factoring: A General Strategy

5.7 Solving Quadratic Equations by Factoring

5.8 Solving Applications

**6. Rational Expression and Equations**

6.1 Rational Expressions

6.2 Multiplication and Division

6.3 Addition, Subtraction, and Least Common Denominators

6.4 Addition and Subtraction with Unlike Denominators

6.5 Complex Rational Expressions

6.6 Rational Equations

6.7 Applications Using Rational Equations and Proportions

**7. Functions and Graphs**

7.1 Introduction to Functions

7.2 Domain and Range

7.3 Graphs of Functions

7.4 The Algebra of Functions

7.5 Formulas, Applications, and Variation

**8. Systems of Linear Equations and Problem Solving**

8.1 Systems of Equations in Two Variables

8.2 Solving by Substitution or Elimination

8.3 Solving Applications: Systems of Two Equations

8.4 Systems of Equations in Three Variables

8.5 Solving Applications: Systems of Three Equations

8.6 Elimination Using Matrices

8.7 Determinants and Cramer’s Rule

8.8 Business and Economics Applications

**9. Inequalities and Problem Solving**

9.1 Inequalities and Applications

9.2 Intersections, Unions, and Compound Inequalities

9.3 Absolute-Value Equations and Inequalities

9.4 Inequalities in Two Variables

9.5 Applications Using Linear Programming

**10. Exponents and Radicals**

10.1 Radical Expressions and Functions

10.2 Rational Numbers as Exponents

10.3 Multiplying Radical Expressions

10.4 Dividing Radical Expressions

10.5 Expressions Containing Several Radical Terms

10.6 Solving Radical Equations

10.7 The Distance Formula, the Midpoint Formula, and Other Applications

10.8 The Complex Numbers

**11. Quadratic Functions and Equations**

11.1 Quadratic Equations

11.2 The Quadratic Formula

11.3 Studying Solutions of Quadratic Equations

11.4 Applications Involving Quadratic Equations

11.5 Equations Reducible to Quadratic

11.6 Quadratic Functions and Their Graphs

11.7 More About Graphing Quadratic Functions

11.8 Problem Solving and Quadratic Functions

11.9 Polynomial Inequalities and Rational Inequalities

**12. Exponential Functions and Logarithmic Functions**

12.1 Composite Functions and Inverse Functions

12.2 Exponential Functions

12.3 Logarithmic Functions

12.4 Properties of Logarithmic Functions

12.5 Common Logarithms and Natural Logarithms

12.6 Solving Exponential Equations and Logarithmic Equations

12.7 Applications of Exponential Functions and Logarithmic Functions

**13. Conic Sections**

13.1 Conic Sections: Parabolas and Circles

13.2 Conic Sections: Ellipses

13.3 Conic Sections: Hyperbolas

13.4 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

**R. Elementary Algebra Review**

R.1 Introduction to Algebraic Expressions

R.2 Equations, Inequalities, and Problem Solving

R.3 Introduction to Graphing

R.4 Polynomials

R.5 Polynomials and Factoring

R6. Rational Expressions and Equations

Appendix A. Mean, Median, and Mode

Appendix B. Sets

Appendix C. Synthetic Division and the Remainder Theorem