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by Arthur Goodman and Lewis Hirsch

Edition: 4TH 98Copyright: 1998

Publisher: Brooks/Cole Publishing Co.

Published: 1998

International: No

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Authors Goodman and Hirsch clearly and carefully develop students' understanding of algebra concepts by using an effective spiral approach. This approach presents a topic at an elementary level and then returns to it at increasing levels of complexity. This gradual introduction builds student confidence while developing concepts, rules, and definitions. To complement this approach, the authors include a wealth of numerical and algebraic examples that reflect a wide variety of situations. These illustrative examples compare and contrast related ideas, helping students understand the sometimes subtle distinctions among various situations.

**1. THE INTEGERS. **

What Is Algebra?

Introduction and Basic Notation.

Integers.

Adding Integers.

Subtracting Integers.

Multiplying and Dividing Integers.

The Real Number System.

Chapter Summary, Review Exercises, and Practice Test.

**2. ALGEBRAIC EXPRESSIONS. **

Variables and Exponents.

Algebraic Substitution.

The Distributive Property and Combining Like Terms.

Simplifying Algebraic Expressions.

Translating Phrases and Sentences Algebraically.

Chapter Summary, Review Exercises, and Practice Test.

**3. FIRST-DEGREE EQUATIONS AND INEQUALITIES. **

Types of Equations and Basic Properties of Equalities.

Solving First-Degree Equations in One Variable and Applications.

More First-Degree Equations and Applications.

Types of Inequalities and Basic Properties of Inequalities.

Solving First-Degree Inequalities in One Variable and Applications.

Chapter Summary, Review Exercises, and Practice Test.

Cumulative Review and Practice Test : Chapters 1-3.

**4. RATIONAL EXPRESSIONS.**

Fundamental Principle of Fractions.

Multiplying and Dividing Rational Expressions.

Adding and Subtracting Rational Expressions.

Solving Fractional Equations and Inequalities.

Ratio and Proportion.

Verbal Problems.

Chapter Summary, Review Exercises, and Practice Test.

**5. GRAPHING STRAIGHT LINES. **

The Rectangular (Cartesian) Coordinate System.

Graphing a Linear Equation in Two Variables.

The Slope.

The Equation of a Line.

**6. INTERPRETING GRAPHS AND SYSTEMS OF LINEAR EQUATIONS. **

Interpreting Graphs.

Solving Systems of Linear Equations : Graphical Method.

Solving Systems of Linear Equations : Algebraic Methods.

Verbal Problems.

Chapter Summary, Review Exercises, and Practice Test.

Cumulative Review and Practice Test : Chapters 4-6.

**7. EXPONENTS AND POLYNOMIALS. **

Exponent Rules.

Zero and Negative Exponents.

Scientific Notation.

Introduction to Polynomials.

Multiplying Polynomials.

Special Products.

Chapter Summary, Review Exercises, and Practice Test.

** 8. FACTORING. **

Common Factors.

Factoring Trinomials.

More Factoring. Solving Polynomial Equations by Factoring.

Dividing Polynomials.

Chapter Summary, Review Exercises, and Practice Test.

**9. MORE RATIONAL EXPRESSIONS. **

Reducing Rational Expressions.

Multiplying and Dividing Rational Expressions.

Adding and Subtracting Rational Expressions.

Fractional Equations.

Literal Equations.

Verbal Problems.

Chapter Summary, Review Exercises, and Practice Test.

Cumulative Review and Practice Test : Chapters 7-9.

**10. RADICAL EXPRESSIONS AND EQUATIONS.**

Definitions and Basic Notation.

Properties of Radicals and Simplest Radical Form.

Adding and Subtracting Radical Expressions.

Multiplying and Dividing Radical Expressions.

Radical Equations.

Chapter Summary, Review Exercises, and Practice Test.

**11. QUADRATIC EQUATIONS. **

The Factoring and Square Root Methods.

The Method of Completing the Square.

The Quadratic Formula. Choosing a Method.

Verbal Problems.

Graphing Quadratic Equations.

Chapter Summary, Review Exercises, and Practice Test.

Cumulative Review and Practice Test : Chapters 10-11.

**12.CHAPTER G. SUPPLEMENTAL CHAPTER ON GEOMETRY. **

Angles.

Triangles.

Quadrilaterals; Perimeter and Area.

Circles.

Solid Geometry.

Appendix A : A Review of Arithmetic.

Appendix B : Using a Scientific Calculator.

Answers to Selected Exercises and Chapter Tests.

Index.

Summary

Authors Goodman and Hirsch clearly and carefully develop students' understanding of algebra concepts by using an effective spiral approach. This approach presents a topic at an elementary level and then returns to it at increasing levels of complexity. This gradual introduction builds student confidence while developing concepts, rules, and definitions. To complement this approach, the authors include a wealth of numerical and algebraic examples that reflect a wide variety of situations. These illustrative examples compare and contrast related ideas, helping students understand the sometimes subtle distinctions among various situations.

Table of Contents

**1. THE INTEGERS. **

What Is Algebra?

Introduction and Basic Notation.

Integers.

Adding Integers.

Subtracting Integers.

Multiplying and Dividing Integers.

The Real Number System.

Chapter Summary, Review Exercises, and Practice Test.

**2. ALGEBRAIC EXPRESSIONS. **

Variables and Exponents.

Algebraic Substitution.

The Distributive Property and Combining Like Terms.

Simplifying Algebraic Expressions.

Translating Phrases and Sentences Algebraically.

Chapter Summary, Review Exercises, and Practice Test.

**3. FIRST-DEGREE EQUATIONS AND INEQUALITIES. **

Types of Equations and Basic Properties of Equalities.

Solving First-Degree Equations in One Variable and Applications.

More First-Degree Equations and Applications.

Types of Inequalities and Basic Properties of Inequalities.

Solving First-Degree Inequalities in One Variable and Applications.

Chapter Summary, Review Exercises, and Practice Test.

Cumulative Review and Practice Test : Chapters 1-3.

**4. RATIONAL EXPRESSIONS.**

Fundamental Principle of Fractions.

Multiplying and Dividing Rational Expressions.

Adding and Subtracting Rational Expressions.

Solving Fractional Equations and Inequalities.

Ratio and Proportion.

Verbal Problems.

Chapter Summary, Review Exercises, and Practice Test.

**5. GRAPHING STRAIGHT LINES. **

The Rectangular (Cartesian) Coordinate System.

Graphing a Linear Equation in Two Variables.

The Slope.

The Equation of a Line.

**6. INTERPRETING GRAPHS AND SYSTEMS OF LINEAR EQUATIONS. **

Interpreting Graphs.

Solving Systems of Linear Equations : Graphical Method.

Solving Systems of Linear Equations : Algebraic Methods.

Verbal Problems.

Chapter Summary, Review Exercises, and Practice Test.

Cumulative Review and Practice Test : Chapters 4-6.

**7. EXPONENTS AND POLYNOMIALS. **

Exponent Rules.

Zero and Negative Exponents.

Scientific Notation.

Introduction to Polynomials.

Multiplying Polynomials.

Special Products.

Chapter Summary, Review Exercises, and Practice Test.

** 8. FACTORING. **

Common Factors.

Factoring Trinomials.

More Factoring. Solving Polynomial Equations by Factoring.

Dividing Polynomials.

Chapter Summary, Review Exercises, and Practice Test.

**9. MORE RATIONAL EXPRESSIONS. **

Reducing Rational Expressions.

Multiplying and Dividing Rational Expressions.

Adding and Subtracting Rational Expressions.

Fractional Equations.

Literal Equations.

Verbal Problems.

Chapter Summary, Review Exercises, and Practice Test.

Cumulative Review and Practice Test : Chapters 7-9.

**10. RADICAL EXPRESSIONS AND EQUATIONS.**

Definitions and Basic Notation.

Properties of Radicals and Simplest Radical Form.

Adding and Subtracting Radical Expressions.

Multiplying and Dividing Radical Expressions.

Radical Equations.

Chapter Summary, Review Exercises, and Practice Test.

**11. QUADRATIC EQUATIONS. **

The Factoring and Square Root Methods.

The Method of Completing the Square.

The Quadratic Formula. Choosing a Method.

Verbal Problems.

Graphing Quadratic Equations.

Chapter Summary, Review Exercises, and Practice Test.

Cumulative Review and Practice Test : Chapters 10-11.

**12.CHAPTER G. SUPPLEMENTAL CHAPTER ON GEOMETRY. **

Angles.

Triangles.

Quadrilaterals; Perimeter and Area.

Circles.

Solid Geometry.

Appendix A : A Review of Arithmetic.

Appendix B : Using a Scientific Calculator.

Answers to Selected Exercises and Chapter Tests.

Index.

Publisher Info

Publisher: Brooks/Cole Publishing Co.

Published: 1998

International: No

Published: 1998

International: No

**1. THE INTEGERS. **

What Is Algebra?

Introduction and Basic Notation.

Integers.

Adding Integers.

Subtracting Integers.

Multiplying and Dividing Integers.

The Real Number System.

Chapter Summary, Review Exercises, and Practice Test.

**2. ALGEBRAIC EXPRESSIONS. **

Variables and Exponents.

Algebraic Substitution.

The Distributive Property and Combining Like Terms.

Simplifying Algebraic Expressions.

Translating Phrases and Sentences Algebraically.

Chapter Summary, Review Exercises, and Practice Test.

**3. FIRST-DEGREE EQUATIONS AND INEQUALITIES. **

Types of Equations and Basic Properties of Equalities.

Solving First-Degree Equations in One Variable and Applications.

More First-Degree Equations and Applications.

Types of Inequalities and Basic Properties of Inequalities.

Solving First-Degree Inequalities in One Variable and Applications.

Chapter Summary, Review Exercises, and Practice Test.

Cumulative Review and Practice Test : Chapters 1-3.

**4. RATIONAL EXPRESSIONS.**

Fundamental Principle of Fractions.

Multiplying and Dividing Rational Expressions.

Adding and Subtracting Rational Expressions.

Solving Fractional Equations and Inequalities.

Ratio and Proportion.

Verbal Problems.

Chapter Summary, Review Exercises, and Practice Test.

**5. GRAPHING STRAIGHT LINES. **

The Rectangular (Cartesian) Coordinate System.

Graphing a Linear Equation in Two Variables.

The Slope.

The Equation of a Line.

**6. INTERPRETING GRAPHS AND SYSTEMS OF LINEAR EQUATIONS. **

Interpreting Graphs.

Solving Systems of Linear Equations : Graphical Method.

Solving Systems of Linear Equations : Algebraic Methods.

Verbal Problems.

Chapter Summary, Review Exercises, and Practice Test.

Cumulative Review and Practice Test : Chapters 4-6.

**7. EXPONENTS AND POLYNOMIALS. **

Exponent Rules.

Zero and Negative Exponents.

Scientific Notation.

Introduction to Polynomials.

Multiplying Polynomials.

Special Products.

Chapter Summary, Review Exercises, and Practice Test.

** 8. FACTORING. **

Common Factors.

Factoring Trinomials.

More Factoring. Solving Polynomial Equations by Factoring.

Dividing Polynomials.

Chapter Summary, Review Exercises, and Practice Test.

**9. MORE RATIONAL EXPRESSIONS. **

Reducing Rational Expressions.

Multiplying and Dividing Rational Expressions.

Adding and Subtracting Rational Expressions.

Fractional Equations.

Literal Equations.

Verbal Problems.

Chapter Summary, Review Exercises, and Practice Test.

Cumulative Review and Practice Test : Chapters 7-9.

**10. RADICAL EXPRESSIONS AND EQUATIONS.**

Definitions and Basic Notation.

Properties of Radicals and Simplest Radical Form.

Adding and Subtracting Radical Expressions.

Multiplying and Dividing Radical Expressions.

Radical Equations.

Chapter Summary, Review Exercises, and Practice Test.

**11. QUADRATIC EQUATIONS. **

The Factoring and Square Root Methods.

The Method of Completing the Square.

The Quadratic Formula. Choosing a Method.

Verbal Problems.

Graphing Quadratic Equations.

Chapter Summary, Review Exercises, and Practice Test.

Cumulative Review and Practice Test : Chapters 10-11.

**12.CHAPTER G. SUPPLEMENTAL CHAPTER ON GEOMETRY. **

Angles.

Triangles.

Quadrilaterals; Perimeter and Area.

Circles.

Solid Geometry.

Appendix A : A Review of Arithmetic.

Appendix B : Using a Scientific Calculator.

Answers to Selected Exercises and Chapter Tests.

Index.