Elementary and Intermediate Algebra: Concepts and Applications, 4th Edition

Note: Each chapter ends with a Study Summary, Review Exercises, and a Chapter Test. A Cumulative Review is provided after Chapters 3, 6, 9, 12, and 14.

 

Chapter 1   Introduction to Algebraic Expressions

Introduction to Algebra

The Commutative, Associative, and Distributive Laws

Fraction Notation

Positive and Negative Real Numbers

Addition of Real Numbers

Subtraction of Real Numbers

Multiplication and Division of Real Numbers

Exponential Notation and Order of Operations

Connecting the Concepts

Chapter 2 Equations, Inequalities, and Problem Solving

Solving Equations

Using the Principles Together

Connecting the Concepts

Formulas

Applications with Percent

Problem Solving

Solving Inequalities

Solving Applications with Inequalities

Chapter 3   Introduction to Graphing

Reading Graphs, Plotting Points, and Scaling Graphs

Graphing Linear Equations

Graphing and Intercepts

Rates

Slope

Slope—Intercept Form

Connecting the Concepts

Point—Slope Form

Connecting the Concepts

Chapter 4   Polynomials

Exponents and Their Properties

Polynomials

Addition and Subtraction of Polynomials

Connecting the Concepts 

Multiplication of Polynomials

Special Products

Polynomials in Several Variables

Division of Polynomials

Negative Exponents and Scientific Notation

Chapter 5   Polynomials and Factoring

Introduction to Factoring

Factoring Trinomials of the Type x² + bx + c

Factoring Trinomials of the Type ax² + bx + c

Factoring Perfect-Square Trinomials and Differences of Squares

Factoring Sums or Differences of Cubes

Factoring: A General Strategy

Connecting the Concepts

Solving Quadratic Equations by Factoring

Connecting the Concepts

Solving Applications

Chapter 6   Rational Expressions and Equations

Rational Expressions

Multiplication and Division

Addition, Subtraction, and Least Common Denominators

Addition and Subtraction with Unlike Denominators

Complex Rational Expressions

Solving Rational Equations

Connecting the Concepts

Applications Using Rational Equations and Proportions

Formulas and Equations

Chapter 7   Functions and Graphs

Introduction to Functions

Domain and Range

Graphs of Functions (including brief review of graphing)

Connecting the Concepts

The Algebra of Functions

Variation and Problem Solving

Chapter 8    Systems of Equations and Problem Solving

Systems of Equations in Two Variables

Solving by Substitution or Elimination

Connecting the Concepts

Solving Applications:   Systems of Two Equations

Systems of Equations in Three Variables

Connecting the Concepts 

Solving Applications:   Systems of Three Equations

Elimination Using Matrices

Determinants and Cramer’s Rule

Business and Economics Applications

Chapter 9   Inequalities and Problem Solving

Interval Notation and Problem Solving

Intersections, Unions, and Compound Inequalities

Absolute-Value Equations and Inequalities

Inequalities in Two Variables

Connecting the Concepts

Applications Using Linear Programming

Chapter 10   Exponents and Radicals

Radical Expressions and Functions

Rational Numbers as Exponents

Multiplying Radical Expressions

Dividing Radical Expressions

Expressions Containing Several Radical Terms

Solving Radical Equations

Connecting the Concepts

Geometric Applications

The Complex Numbers

Chapter 11   Quadratic Functions and Equations

Quadratic Equations

The Quadratic Formula

Applications Involving Quadratic Equations

Studying Solutions of Quadratic Equations

Equations Reducible to Quadratic

Quadratic Functions and Their Graphs

Connecting the Concepts

More About Graphing Quadratic Functions

Problem Solving and Quadratic Functions

Polynomial and Rational Inequalities

Chapter 12   Exponential and Logarithmic Functions

Composite and Inverse Functions

Exponential Functions

Connecting the Concepts

Logarithmic Functions

Properties of Logarithmic Functions

Common and Natural Logarithms

Solving Exponential and Logarithmic Equations

Applications of Exponential and Logarithmic Functions

Chapter 13       Conic Sections

Conic Sections: Parabolas and Circles

Conic Sections: Ellipses

Conic Sections: Hyperbolas

Connecting the Concepts 

Nonlinear Systems of Equations

Chapter 14       Sequences, Series, and The Binomial Theorem

Sequences and Series

Arithmetic Sequences and Series

Geometric Sequences and Series

The Binomial Theorem

Connecting the Concepts

Chapter R   Elementary Algebra Review

Introduction to Algebraic Expressions

Equations, Inequalities, and Problem Solving

Introduction to Graphing

Polynomials

Polynomials and Factoring Rational Expressions and Equations

 

Appendix A:  Sets

Appendix B:  Synthetic Division

Table 1:          Fractional and Decimal Equivalents

Table 2:          Squares and Square Roots

Table 3:          Geometric Formulas

Answers

Glossary

Index

Index of Applications