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by Ron Larson and Robert P. Hostetler

Edition: 4TH 05Copyright: 2005

Publisher: Houghton Mifflin Harcourt

Published: 2005

International: No

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Designed for first-year developmental students who need support in intermediate algebra, the Fourth Edition of Intermediate Algebra retains the hallmark features for which the Larson team is known: abundant, high-quality applications; the use of real data; the integration of visualization (figures and graphs) throughout; and extensive opportunities for self-assessment (mid-chapter quizzes, review exercises, tests, and cumulative tests). In developing supportive new features for the Fourth Edition, the authors' goal is for students to come away from the class with a firm understanding of algebra and how it functions as a modern modeling language.

- New! What You Should Learn orients students to each section by listing the main objectives.
- New! Why You Should Learn It provides a motivational explanation for learning the given objectives.
- New! What Did You Learn? following each chapter highlights key mathematical terms and concepts. For easy reference, Key Terms are correlated to the chapter by page number, while Key Concepts are correlated by section number.
- Integrated Review Exercises appear before section exercises in every section. They offer a review of skills, definitions, and problem solving from previous chapters.
- Skill-Building Exercises have increased in number and type. These exercises provide a broad range of computational, conceptual, and applied problems to help students master several types of skills.
- Exercises Keyed to Examples facilitate navigation of the text by referring students back to an example at the beginning of the section.
- Section Objectives are listed at the beginning of sections and at point of use throughout the chapter. Students can refer to them easily, checking to see if they've mastered one objective before moving on to the next one.
- Revised! Definitions are clearer and Key Concepts are emphasized in boxes, allowing students to expand their math vocabulary as they progress through the chapter.
- Review Exercises are keyed by section and split into two categories: Reviewing Skills and Solving Problems. This allows students to see which sections they have mastered and which need more work before taking any exams or quizzes. It also lets professors assign review problems according to sections completed.
- Carefully graded section exercises organized into three categories include: Developing Skills, Solving Problems, and Explaining Concepts. This progression in level of difficulty gives students the opportunity to master one level of problem solving before moving on to the next.
- Motivating the Chapter sections in chapter opener offer real-life, multi-part problems that require students to synthesize the skills learned in the entire chapter. Students can examine the problem at the beginning of the chapter, then return to it and solve it when they've mastered the necessary skills. The problem is broken up into sections that are keyed to specific exercises and section sets, so instructors can assign the problem in pieces as part of a homework assignment or as collaborative work for student projects.
- Application problems use data from real life to demonstrate the relevance of algebra in the real world. These problems, updated to reflect current statistics and information, enable students to see where data is derived from and relate to the use of mathematics in contemporary society.
- Revised! Technology: Tips offer instruction at point of use for using technology to visualize concepts, perform computations, and verify solutions.
- Revised! Technology: Discovery engages students in using technology to explore mathematical concepts and discover patterns and mathematical relationships.
- Mid-Chapter Quizzes, Chapter Tests, and Cumulative Tests provide a wide array of self-assessment tools for students to measure their progress.
- Discussing the Concept activities offer instructors flexible options for assigning as individual homework, collaborative work, or class discussion. In the Instructor's Edition, many of these problems have been identified with a special icon as alternative discussion/collaborative problems.

**Larson, Ron : The Pennsylvania State University, The Behrend College**

Ron Larson received his Ph.D. in mathematics from the University of Colorado and has been a professor of mathematics at The Pennsylvania State University since 1970. He has pioneered the use of multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson has also conducted numerous seminars and in-service workshops for math teachers around the country about the use of computer technology as a teaching tool and motivational aid. His Interactive Calculus(a complete text on CD-ROM) received the 1996 Texty Award for the most innovative mathematics instructional material at the college level. It is currently the first mainstream college textbook to be offered on the Internet.

Hostetler, Robert P. : The Pennsylvania State University, The Behrend College

** **Bob Hostetler received his Ph.D. in Mathematics from The Pennsylvania State University in 1970. He has taught at Penn State for many years and has authored several calculus, precalculus, and intermediate algebra textbooks. His teaching specialties include Remedial Algebra, Calculus, Math Education and his research interests include mathematics education and textbooks.

*Note: Each chapter begins with "Motivating the Chapter," includes a Mid-Chapter Quiz, and concludes with "What Did You Learn?" (chapter summary), Review Exercises, and a Chapter Test.*

1. Fundamentals of Algebra

1.1 The Real Number System

1.2 Operations with Real Numbers

1.3 Properties of Real Numbers

1.4 Algebraic Expressions

1.5 Constructing Algebraic Expressions

2. Linear Equations and Inequalities

2.1 Linear Equations

2.2 Linear Equations and Problem Solving

2.3 Business and Scientific Problems

2.4 Linear Inequalities

2.5 Absolute Value Equations and Inequalities

3. Graphs and Functions

3.1 The Rectangular Coordinate System

3.2 Graphs of Equations

3.3 Slope and Graphs of Linear Equations

3.4 Equations of Lines

3.5 Graphs of Linear Inequalities

3.6 Relations and Functions

3.7 Graphs of Functions

4. Systems of Equations and Inequalities

4.1 Systems of Equations

4.2 Linear Systems in Two Variables

4.3 Linear Systems in Three Variables

4.4 Matrices and Linear Systems

4.5 Determinants and Linear Systems

4.6 Systems of Linear Inequalities

Cumulative Test: Chapters 1-4

5. Polynomials and Factoring

5.1 Integer Exponents and Scientific Notation

5.2 Adding and Subtracting Polynomials

5.3 Multiplying Polynomials

5.4 Factoring by Grouping and Special Forms

5.5 Factoring Trinomials

5.6 Solving Polynomial Equations by Factoring

6. Rational Expressions, Equations, and Functions

6.1 Rational Expressions and Functions

6.2 Multiplying and Dividing Rational Expressions

6.3 Adding and Subtracting Rational Expressions

6.4 Complex Fractions

6.5 Dividing Polynomials and Synthetic Division

6.6 Solving Rational Equations

6.7 Applications and Variation

7. Radicals and Complex Numbers

7.1 Radicals and Rational Exponents

7.2 Simplifying Radical Expressions

7.3 Adding and Subtracting Radical Expressions

7.4 Mulitplying and Dividing Radical Expressions

7.5 Radical Equations and Applications

7.6 Complex Numbers

Cumulative Test: Chapters 5-7

8. Quadratic Equations, Functions, and Inequalities

8.1 Solving Quadratic Equations: Factoring and Special Forms

8.2 Completing the Square

8.3 The Quadratic Formula

8.4 Graphs of Quadratic Functions

8.5 Applications of Quadratic Equations

8.6 Quadratic and Rational Inequalities

9. Exponential and Logarithmic Functions

9.1 Exponential Functions

9.2 Composite and Inverse Functions

9.3 Logarithmic Functions

9.4 Properties of Logarithms

9.5 Solving Exponential and Logarithmic Equations

9.6 Applications

10. Conics

10.1 Circles and Parabolas

10.2 Ellipses

10.3 Hyperbolas

10.4 Solving Nonlinear Systems of Equations

Cumulative Test: Chapters 8-10

11. Sequences, Series, and the Binomial Theorem

11.1 Sequences and Series

11.2 Arithmetic Sequences

11.3 Geometric Sequences and Series

11.4 The Binomial Theorem

Appendix A. Introduction to Graphing Calculators

Appendix B. Further Concepts in Geometry (web)

B.1 Exploring Congruence and Similarity

B.2 Angles

Appendix C. Further Concepts in Statistics (web)

Appendix D. Introduction to Logic (web)

D.1 Statements and Truth Tables

D.2 Implications, Quantifiers, and Venn Diagrams

D.3 Logical Arguments

Appendix E. Counting Principles (web)

Appendix F. Probability (web)

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Summary

Designed for first-year developmental students who need support in intermediate algebra, the Fourth Edition of Intermediate Algebra retains the hallmark features for which the Larson team is known: abundant, high-quality applications; the use of real data; the integration of visualization (figures and graphs) throughout; and extensive opportunities for self-assessment (mid-chapter quizzes, review exercises, tests, and cumulative tests). In developing supportive new features for the Fourth Edition, the authors' goal is for students to come away from the class with a firm understanding of algebra and how it functions as a modern modeling language.

- New! What You Should Learn orients students to each section by listing the main objectives.
- New! Why You Should Learn It provides a motivational explanation for learning the given objectives.
- New! What Did You Learn? following each chapter highlights key mathematical terms and concepts. For easy reference, Key Terms are correlated to the chapter by page number, while Key Concepts are correlated by section number.
- Integrated Review Exercises appear before section exercises in every section. They offer a review of skills, definitions, and problem solving from previous chapters.
- Skill-Building Exercises have increased in number and type. These exercises provide a broad range of computational, conceptual, and applied problems to help students master several types of skills.
- Exercises Keyed to Examples facilitate navigation of the text by referring students back to an example at the beginning of the section.
- Section Objectives are listed at the beginning of sections and at point of use throughout the chapter. Students can refer to them easily, checking to see if they've mastered one objective before moving on to the next one.
- Revised! Definitions are clearer and Key Concepts are emphasized in boxes, allowing students to expand their math vocabulary as they progress through the chapter.
- Review Exercises are keyed by section and split into two categories: Reviewing Skills and Solving Problems. This allows students to see which sections they have mastered and which need more work before taking any exams or quizzes. It also lets professors assign review problems according to sections completed.
- Carefully graded section exercises organized into three categories include: Developing Skills, Solving Problems, and Explaining Concepts. This progression in level of difficulty gives students the opportunity to master one level of problem solving before moving on to the next.
- Motivating the Chapter sections in chapter opener offer real-life, multi-part problems that require students to synthesize the skills learned in the entire chapter. Students can examine the problem at the beginning of the chapter, then return to it and solve it when they've mastered the necessary skills. The problem is broken up into sections that are keyed to specific exercises and section sets, so instructors can assign the problem in pieces as part of a homework assignment or as collaborative work for student projects.
- Application problems use data from real life to demonstrate the relevance of algebra in the real world. These problems, updated to reflect current statistics and information, enable students to see where data is derived from and relate to the use of mathematics in contemporary society.
- Revised! Technology: Tips offer instruction at point of use for using technology to visualize concepts, perform computations, and verify solutions.
- Revised! Technology: Discovery engages students in using technology to explore mathematical concepts and discover patterns and mathematical relationships.
- Mid-Chapter Quizzes, Chapter Tests, and Cumulative Tests provide a wide array of self-assessment tools for students to measure their progress.
- Discussing the Concept activities offer instructors flexible options for assigning as individual homework, collaborative work, or class discussion. In the Instructor's Edition, many of these problems have been identified with a special icon as alternative discussion/collaborative problems.

Author Bio

**Larson, Ron : The Pennsylvania State University, The Behrend College**

Ron Larson received his Ph.D. in mathematics from the University of Colorado and has been a professor of mathematics at The Pennsylvania State University since 1970. He has pioneered the use of multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson has also conducted numerous seminars and in-service workshops for math teachers around the country about the use of computer technology as a teaching tool and motivational aid. His Interactive Calculus(a complete text on CD-ROM) received the 1996 Texty Award for the most innovative mathematics instructional material at the college level. It is currently the first mainstream college textbook to be offered on the Internet.

Hostetler, Robert P. : The Pennsylvania State University, The Behrend College

** **Bob Hostetler received his Ph.D. in Mathematics from The Pennsylvania State University in 1970. He has taught at Penn State for many years and has authored several calculus, precalculus, and intermediate algebra textbooks. His teaching specialties include Remedial Algebra, Calculus, Math Education and his research interests include mathematics education and textbooks.

Table of Contents

*Note: Each chapter begins with "Motivating the Chapter," includes a Mid-Chapter Quiz, and concludes with "What Did You Learn?" (chapter summary), Review Exercises, and a Chapter Test.*

1. Fundamentals of Algebra

1.1 The Real Number System

1.2 Operations with Real Numbers

1.3 Properties of Real Numbers

1.4 Algebraic Expressions

1.5 Constructing Algebraic Expressions

2. Linear Equations and Inequalities

2.1 Linear Equations

2.2 Linear Equations and Problem Solving

2.3 Business and Scientific Problems

2.4 Linear Inequalities

2.5 Absolute Value Equations and Inequalities

3. Graphs and Functions

3.1 The Rectangular Coordinate System

3.2 Graphs of Equations

3.3 Slope and Graphs of Linear Equations

3.4 Equations of Lines

3.5 Graphs of Linear Inequalities

3.6 Relations and Functions

3.7 Graphs of Functions

4. Systems of Equations and Inequalities

4.1 Systems of Equations

4.2 Linear Systems in Two Variables

4.3 Linear Systems in Three Variables

4.4 Matrices and Linear Systems

4.5 Determinants and Linear Systems

4.6 Systems of Linear Inequalities

Cumulative Test: Chapters 1-4

5. Polynomials and Factoring

5.1 Integer Exponents and Scientific Notation

5.2 Adding and Subtracting Polynomials

5.3 Multiplying Polynomials

5.4 Factoring by Grouping and Special Forms

5.5 Factoring Trinomials

5.6 Solving Polynomial Equations by Factoring

6. Rational Expressions, Equations, and Functions

6.1 Rational Expressions and Functions

6.2 Multiplying and Dividing Rational Expressions

6.3 Adding and Subtracting Rational Expressions

6.4 Complex Fractions

6.5 Dividing Polynomials and Synthetic Division

6.6 Solving Rational Equations

6.7 Applications and Variation

7. Radicals and Complex Numbers

7.1 Radicals and Rational Exponents

7.2 Simplifying Radical Expressions

7.3 Adding and Subtracting Radical Expressions

7.4 Mulitplying and Dividing Radical Expressions

7.5 Radical Equations and Applications

7.6 Complex Numbers

Cumulative Test: Chapters 5-7

8. Quadratic Equations, Functions, and Inequalities

8.1 Solving Quadratic Equations: Factoring and Special Forms

8.2 Completing the Square

8.3 The Quadratic Formula

8.4 Graphs of Quadratic Functions

8.5 Applications of Quadratic Equations

8.6 Quadratic and Rational Inequalities

9. Exponential and Logarithmic Functions

9.1 Exponential Functions

9.2 Composite and Inverse Functions

9.3 Logarithmic Functions

9.4 Properties of Logarithms

9.5 Solving Exponential and Logarithmic Equations

9.6 Applications

10. Conics

10.1 Circles and Parabolas

10.2 Ellipses

10.3 Hyperbolas

10.4 Solving Nonlinear Systems of Equations

Cumulative Test: Chapters 8-10

11. Sequences, Series, and the Binomial Theorem

11.1 Sequences and Series

11.2 Arithmetic Sequences

11.3 Geometric Sequences and Series

11.4 The Binomial Theorem

Appendix A. Introduction to Graphing Calculators

Appendix B. Further Concepts in Geometry (web)

B.1 Exploring Congruence and Similarity

B.2 Angles

Appendix C. Further Concepts in Statistics (web)

Appendix D. Introduction to Logic (web)

D.1 Statements and Truth Tables

D.2 Implications, Quantifiers, and Venn Diagrams

D.3 Logical Arguments

Appendix E. Counting Principles (web)

Appendix F. Probability (web)

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 2005

International: No

Published: 2005

International: No

Designed for first-year developmental students who need support in intermediate algebra, the Fourth Edition of Intermediate Algebra retains the hallmark features for which the Larson team is known: abundant, high-quality applications; the use of real data; the integration of visualization (figures and graphs) throughout; and extensive opportunities for self-assessment (mid-chapter quizzes, review exercises, tests, and cumulative tests). In developing supportive new features for the Fourth Edition, the authors' goal is for students to come away from the class with a firm understanding of algebra and how it functions as a modern modeling language.

- New! What You Should Learn orients students to each section by listing the main objectives.
- New! Why You Should Learn It provides a motivational explanation for learning the given objectives.
- New! What Did You Learn? following each chapter highlights key mathematical terms and concepts. For easy reference, Key Terms are correlated to the chapter by page number, while Key Concepts are correlated by section number.
- Integrated Review Exercises appear before section exercises in every section. They offer a review of skills, definitions, and problem solving from previous chapters.
- Skill-Building Exercises have increased in number and type. These exercises provide a broad range of computational, conceptual, and applied problems to help students master several types of skills.
- Exercises Keyed to Examples facilitate navigation of the text by referring students back to an example at the beginning of the section.
- Section Objectives are listed at the beginning of sections and at point of use throughout the chapter. Students can refer to them easily, checking to see if they've mastered one objective before moving on to the next one.
- Revised! Definitions are clearer and Key Concepts are emphasized in boxes, allowing students to expand their math vocabulary as they progress through the chapter.
- Review Exercises are keyed by section and split into two categories: Reviewing Skills and Solving Problems. This allows students to see which sections they have mastered and which need more work before taking any exams or quizzes. It also lets professors assign review problems according to sections completed.
- Carefully graded section exercises organized into three categories include: Developing Skills, Solving Problems, and Explaining Concepts. This progression in level of difficulty gives students the opportunity to master one level of problem solving before moving on to the next.
- Motivating the Chapter sections in chapter opener offer real-life, multi-part problems that require students to synthesize the skills learned in the entire chapter. Students can examine the problem at the beginning of the chapter, then return to it and solve it when they've mastered the necessary skills. The problem is broken up into sections that are keyed to specific exercises and section sets, so instructors can assign the problem in pieces as part of a homework assignment or as collaborative work for student projects.
- Application problems use data from real life to demonstrate the relevance of algebra in the real world. These problems, updated to reflect current statistics and information, enable students to see where data is derived from and relate to the use of mathematics in contemporary society.
- Revised! Technology: Tips offer instruction at point of use for using technology to visualize concepts, perform computations, and verify solutions.
- Revised! Technology: Discovery engages students in using technology to explore mathematical concepts and discover patterns and mathematical relationships.
- Mid-Chapter Quizzes, Chapter Tests, and Cumulative Tests provide a wide array of self-assessment tools for students to measure their progress.
- Discussing the Concept activities offer instructors flexible options for assigning as individual homework, collaborative work, or class discussion. In the Instructor's Edition, many of these problems have been identified with a special icon as alternative discussion/collaborative problems.

**Larson, Ron : The Pennsylvania State University, The Behrend College**

Ron Larson received his Ph.D. in mathematics from the University of Colorado and has been a professor of mathematics at The Pennsylvania State University since 1970. He has pioneered the use of multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson has also conducted numerous seminars and in-service workshops for math teachers around the country about the use of computer technology as a teaching tool and motivational aid. His Interactive Calculus(a complete text on CD-ROM) received the 1996 Texty Award for the most innovative mathematics instructional material at the college level. It is currently the first mainstream college textbook to be offered on the Internet.

Hostetler, Robert P. : The Pennsylvania State University, The Behrend College

** **Bob Hostetler received his Ph.D. in Mathematics from The Pennsylvania State University in 1970. He has taught at Penn State for many years and has authored several calculus, precalculus, and intermediate algebra textbooks. His teaching specialties include Remedial Algebra, Calculus, Math Education and his research interests include mathematics education and textbooks.

*Note: Each chapter begins with "Motivating the Chapter," includes a Mid-Chapter Quiz, and concludes with "What Did You Learn?" (chapter summary), Review Exercises, and a Chapter Test.*

1. Fundamentals of Algebra

1.1 The Real Number System

1.2 Operations with Real Numbers

1.3 Properties of Real Numbers

1.4 Algebraic Expressions

1.5 Constructing Algebraic Expressions

2. Linear Equations and Inequalities

2.1 Linear Equations

2.2 Linear Equations and Problem Solving

2.3 Business and Scientific Problems

2.4 Linear Inequalities

2.5 Absolute Value Equations and Inequalities

3. Graphs and Functions

3.1 The Rectangular Coordinate System

3.2 Graphs of Equations

3.3 Slope and Graphs of Linear Equations

3.4 Equations of Lines

3.5 Graphs of Linear Inequalities

3.6 Relations and Functions

3.7 Graphs of Functions

4. Systems of Equations and Inequalities

4.1 Systems of Equations

4.2 Linear Systems in Two Variables

4.3 Linear Systems in Three Variables

4.4 Matrices and Linear Systems

4.5 Determinants and Linear Systems

4.6 Systems of Linear Inequalities

Cumulative Test: Chapters 1-4

5. Polynomials and Factoring

5.1 Integer Exponents and Scientific Notation

5.2 Adding and Subtracting Polynomials

5.3 Multiplying Polynomials

5.4 Factoring by Grouping and Special Forms

5.5 Factoring Trinomials

5.6 Solving Polynomial Equations by Factoring

6. Rational Expressions, Equations, and Functions

6.1 Rational Expressions and Functions

6.2 Multiplying and Dividing Rational Expressions

6.3 Adding and Subtracting Rational Expressions

6.4 Complex Fractions

6.5 Dividing Polynomials and Synthetic Division

6.6 Solving Rational Equations

6.7 Applications and Variation

7. Radicals and Complex Numbers

7.1 Radicals and Rational Exponents

7.2 Simplifying Radical Expressions

7.3 Adding and Subtracting Radical Expressions

7.4 Mulitplying and Dividing Radical Expressions

7.5 Radical Equations and Applications

7.6 Complex Numbers

Cumulative Test: Chapters 5-7

8. Quadratic Equations, Functions, and Inequalities

8.1 Solving Quadratic Equations: Factoring and Special Forms

8.2 Completing the Square

8.3 The Quadratic Formula

8.4 Graphs of Quadratic Functions

8.5 Applications of Quadratic Equations

8.6 Quadratic and Rational Inequalities

9. Exponential and Logarithmic Functions

9.1 Exponential Functions

9.2 Composite and Inverse Functions

9.3 Logarithmic Functions

9.4 Properties of Logarithms

9.5 Solving Exponential and Logarithmic Equations

9.6 Applications

10. Conics

10.1 Circles and Parabolas

10.2 Ellipses

10.3 Hyperbolas

10.4 Solving Nonlinear Systems of Equations

Cumulative Test: Chapters 8-10

11. Sequences, Series, and the Binomial Theorem

11.1 Sequences and Series

11.2 Arithmetic Sequences

11.3 Geometric Sequences and Series

11.4 The Binomial Theorem

Appendix A. Introduction to Graphing Calculators

Appendix B. Further Concepts in Geometry (web)

B.1 Exploring Congruence and Similarity

B.2 Angles

Appendix C. Further Concepts in Statistics (web)

Appendix D. Introduction to Logic (web)

D.1 Statements and Truth Tables

D.2 Implications, Quantifiers, and Venn Diagrams

D.3 Logical Arguments

Appendix E. Counting Principles (web)

Appendix F. Probability (web)