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by Donald Hutchison, Barry Bergman and Louis Hoelzle

Edition: 2ND 04Copyright: 2004

Publisher: McGraw-Hill Publishing Company

Published: 2004

International: No

Donald Hutchison, Barry Bergman and Louis Hoelzle

Edition: 2ND 04
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A Unified Text That Serves Your Needs. Most colleges offering elementary and intermediate algebra use two different texts, one for each course. As a result, students may be required to purchase two texts; this can result in a considerable amount of topic overlap. Over the last few years, several publishers have issued "combined" texts that take chapters from two texts and merge them into a single book. This has allowed students to purchase a single text, but it has done little to reduce the overlap. The goal of this author team has been to produce a text that was more than a combined text. They wanted to unify the topics and themes of beginning and intermediate algebra in a fluid, non-repetitive text. We also wanted to produce a text that will prepare students from different mathematical backgrounds for college algebra. We believe we have accomplished our goals. For students entering directly from an arithmetic or pre-algebra course, this is a text that contains all of the material needed to prepare for college algebra. It can be offered in two quarters or in two semesters. The new Review Chapter found between chapters 6 and 7 serves as a mid-book review for students preparing to take a final exam that covers the first seven chapters. Finally, we have produced a text that will accommodate those students placing into the second term of a two-term sequence. Here is where the Review Chapter is most valuable. It gives the students an opportunity to check that they have all of the background required to begin in Chapter 7. If the students struggle with any of the material in the Review Chapter, they are referred to the appropriate section for further review.

**New to This Edition **

- A new Review Chapter replaces "Moving to the Intermediate Algebra Level." The Review Chapter provides a concise, comprehensive review of chapters 1 through 6. The chapter contains review exercises and section references.
- Overcoming Math Anxiety Boxes--Located within the first few chapters are suggestions on overcoming math anxiety. These suggestions are designed to be timely and useful, The are the same suggestions most instructors make in class, but sometimes those words are given extra weight when students see them in print.
- The chapter on functions now follows the chapter on polynomials.
- Several new sections have been added to the text:
- Problem Solving with Factoring
- A General Strategy for Factoring
- Rational Functions
- Solving Radical Equations

**Features **

- As the subtitle implies, Hutchison et al. "unifies" elementary algebra and intermediate algebra, reducing repetition that occurs within some combined texts.
- Visualization encouraged through graphing and concrete models.
- Problem solving taught through numerous examples carefully worked out, with a matched "Check Yourself" exercise after each example.

**Hutchison, Donald : Clackamas Community College **

Bergman, Barry : Clackamas Community College

** Hoelzle, Louis : Bucks County Community College **

0 Prealgebra Review

0.1 A Review of Fractions

0.2 Real Numbers

0.3 Adding and Subtracting Real Numbers

0.4 Multiplying and Dividing Real Numbers

0.5 Exponents and Order of Operation

1 From Arithmetic to Algebra

1.1 Transition to Algebra

1.2 Evaluating Algebraic Expressions

1.3 Adding and Subtracting Algebraic Expressions

1.4 Sets

2 Equations and Inequalities

2.1 Solving Equations by Adding and Subtracting

2.2 Solving Equations by Multiplying and Dividing

2.3 Combining the Rules to Solve Equations

2.4 Literal Equations and Their Applications

2.5 Solving Linear Inequalities Using Addition

2.6 Solving Linear Inequalities Using Multiplication

2.7 Solving Absolute Value Equations (Optional)

2.8 Solving Absolute Value Inequalities (Optional)

3 Graphs and Linear Equations

3.1 Solutions of Equations in Two Variables

3.2 The Cartesian Coordinate System

3.3 The Graph of a Linear Equation

3.4 The Slope of a Line

3.5 Forms of Linear Equations

4 Exponents and Polynomials

4.1 Positive Integer Exponents

4.2 Zero and Negative Exponents and Scientific Notation

4.3 Introduction to Polynomials

4.4 Addition and Subtraction of Polynomials

4.5 Multiplication of Polynomials and Special Products

4.6 Division of Polynomials

5 A Beginning Look at Functions

5.1 Relations and Functions

5.2 Tables and Graphs

5.3 Algebra of Functions

5.4 Composition of Functions

6 Factoring Polynomials

6.1 An Introduction to Factoring

6.2 Factoring Special Polynomials

6.3 Factoring Trinomials: The ac method

6.3* Factoring Trinomials: Trial and Error

6.4 Solving Quadratic Equations by Factoring

6.5 Problem Solving with Factoring

6.6 A General Strategy for Factoring

R A Review of Elementary Algebra

R.1 From Arithmetic to Algebra

R.2 Equations and Inequalities

R.3 Graphs and Linear Equations

R.4 Exponents and Polynomials

R.5 A Beginning Look at Functions

R.6 Factoring Polynomials

7 Rational Expressions

7.1 Simplifying Rational Expressions

7.2 Multiplication and Division of Rational Expressions

7.3 Addition and Subtraction of Rational Expressions

7.4 Complex Fractions

7.5 Solving Rational Expressions

7.6 Solving Rational Inequalities

7.7 Rational Functions

8 Systems of Linear Equations and Inequalities

8.1 Solving Systems of Linear Equations by Graphing

8.2 Systems of Equations in Two Variables with Applications

8.3 Systems of Linear Equations in Three Variables

8.4 Matrices (Optional)

8.5 Graphing Linear Inequalities in Two Variables

8.6 Systems of Linear Inequalities in Two Variables

9 Graphical Solutions

9.1 Solving Equations in One Variable Graphically

9.2 Solving Linear Inequalities in One Variable Graphically

9.3 Solving Absolute Value Equations Graphically

9.4 Solving Absolute Value Inequalities Graphically

10 Radicals and Exponents

10.1 Roots and Radicals

10.2 Simplifying Radical Expressions

10.3 Operations on Radical Expressions

10.4 Solving Radical Equations

10.5 Rational Exponents

10.6 Complex Numbers

11 Quadratic Functions

11.1 Solving Quadratic Equations by Completing the Square

11.2 The Quadratic Formula

11.3 Solving Quadratic Equations by Graphing

11.4 Solving Quadratic Inequalities

12 Conic Sections

12.1 More on the Parabola

12.2 The Circle

12.3 Ellipses

12.4 Hyperbolas

13 Exponential and Logarithmic Functions

13.1 Inverse Relations and Functions

13.2 Exponential Functions

13.3 Logarithmic Functions

13.4 Properties of Logarithms

13.5 Logarithmic and Exponential Equations

Appendix A

Appendix A.1 Determinants and Cramer's Rule

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Summary

A Unified Text That Serves Your Needs. Most colleges offering elementary and intermediate algebra use two different texts, one for each course. As a result, students may be required to purchase two texts; this can result in a considerable amount of topic overlap. Over the last few years, several publishers have issued "combined" texts that take chapters from two texts and merge them into a single book. This has allowed students to purchase a single text, but it has done little to reduce the overlap. The goal of this author team has been to produce a text that was more than a combined text. They wanted to unify the topics and themes of beginning and intermediate algebra in a fluid, non-repetitive text. We also wanted to produce a text that will prepare students from different mathematical backgrounds for college algebra. We believe we have accomplished our goals. For students entering directly from an arithmetic or pre-algebra course, this is a text that contains all of the material needed to prepare for college algebra. It can be offered in two quarters or in two semesters. The new Review Chapter found between chapters 6 and 7 serves as a mid-book review for students preparing to take a final exam that covers the first seven chapters. Finally, we have produced a text that will accommodate those students placing into the second term of a two-term sequence. Here is where the Review Chapter is most valuable. It gives the students an opportunity to check that they have all of the background required to begin in Chapter 7. If the students struggle with any of the material in the Review Chapter, they are referred to the appropriate section for further review.

**New to This Edition **

- A new Review Chapter replaces "Moving to the Intermediate Algebra Level." The Review Chapter provides a concise, comprehensive review of chapters 1 through 6. The chapter contains review exercises and section references.
- Overcoming Math Anxiety Boxes--Located within the first few chapters are suggestions on overcoming math anxiety. These suggestions are designed to be timely and useful, The are the same suggestions most instructors make in class, but sometimes those words are given extra weight when students see them in print.
- The chapter on functions now follows the chapter on polynomials.
- Several new sections have been added to the text:
- Problem Solving with Factoring
- A General Strategy for Factoring
- Rational Functions
- Solving Radical Equations

**Features **

- As the subtitle implies, Hutchison et al. "unifies" elementary algebra and intermediate algebra, reducing repetition that occurs within some combined texts.
- Visualization encouraged through graphing and concrete models.
- Problem solving taught through numerous examples carefully worked out, with a matched "Check Yourself" exercise after each example.

Author Bio

**Hutchison, Donald : Clackamas Community College **

Bergman, Barry : Clackamas Community College

** Hoelzle, Louis : Bucks County Community College **

Table of Contents

0 Prealgebra Review

0.1 A Review of Fractions

0.2 Real Numbers

0.3 Adding and Subtracting Real Numbers

0.4 Multiplying and Dividing Real Numbers

0.5 Exponents and Order of Operation

1 From Arithmetic to Algebra

1.1 Transition to Algebra

1.2 Evaluating Algebraic Expressions

1.3 Adding and Subtracting Algebraic Expressions

1.4 Sets

2 Equations and Inequalities

2.1 Solving Equations by Adding and Subtracting

2.2 Solving Equations by Multiplying and Dividing

2.3 Combining the Rules to Solve Equations

2.4 Literal Equations and Their Applications

2.5 Solving Linear Inequalities Using Addition

2.6 Solving Linear Inequalities Using Multiplication

2.7 Solving Absolute Value Equations (Optional)

2.8 Solving Absolute Value Inequalities (Optional)

3 Graphs and Linear Equations

3.1 Solutions of Equations in Two Variables

3.2 The Cartesian Coordinate System

3.3 The Graph of a Linear Equation

3.4 The Slope of a Line

3.5 Forms of Linear Equations

4 Exponents and Polynomials

4.1 Positive Integer Exponents

4.2 Zero and Negative Exponents and Scientific Notation

4.3 Introduction to Polynomials

4.4 Addition and Subtraction of Polynomials

4.5 Multiplication of Polynomials and Special Products

4.6 Division of Polynomials

5 A Beginning Look at Functions

5.1 Relations and Functions

5.2 Tables and Graphs

5.3 Algebra of Functions

5.4 Composition of Functions

6 Factoring Polynomials

6.1 An Introduction to Factoring

6.2 Factoring Special Polynomials

6.3 Factoring Trinomials: The ac method

6.3* Factoring Trinomials: Trial and Error

6.4 Solving Quadratic Equations by Factoring

6.5 Problem Solving with Factoring

6.6 A General Strategy for Factoring

R A Review of Elementary Algebra

R.1 From Arithmetic to Algebra

R.2 Equations and Inequalities

R.3 Graphs and Linear Equations

R.4 Exponents and Polynomials

R.5 A Beginning Look at Functions

R.6 Factoring Polynomials

7 Rational Expressions

7.1 Simplifying Rational Expressions

7.2 Multiplication and Division of Rational Expressions

7.3 Addition and Subtraction of Rational Expressions

7.4 Complex Fractions

7.5 Solving Rational Expressions

7.6 Solving Rational Inequalities

7.7 Rational Functions

8 Systems of Linear Equations and Inequalities

8.1 Solving Systems of Linear Equations by Graphing

8.2 Systems of Equations in Two Variables with Applications

8.3 Systems of Linear Equations in Three Variables

8.4 Matrices (Optional)

8.5 Graphing Linear Inequalities in Two Variables

8.6 Systems of Linear Inequalities in Two Variables

9 Graphical Solutions

9.1 Solving Equations in One Variable Graphically

9.2 Solving Linear Inequalities in One Variable Graphically

9.3 Solving Absolute Value Equations Graphically

9.4 Solving Absolute Value Inequalities Graphically

10 Radicals and Exponents

10.1 Roots and Radicals

10.2 Simplifying Radical Expressions

10.3 Operations on Radical Expressions

10.4 Solving Radical Equations

10.5 Rational Exponents

10.6 Complex Numbers

11 Quadratic Functions

11.1 Solving Quadratic Equations by Completing the Square

11.2 The Quadratic Formula

11.3 Solving Quadratic Equations by Graphing

11.4 Solving Quadratic Inequalities

12 Conic Sections

12.1 More on the Parabola

12.2 The Circle

12.3 Ellipses

12.4 Hyperbolas

13 Exponential and Logarithmic Functions

13.1 Inverse Relations and Functions

13.2 Exponential Functions

13.3 Logarithmic Functions

13.4 Properties of Logarithms

13.5 Logarithmic and Exponential Equations

Appendix A

Appendix A.1 Determinants and Cramer's Rule

Publisher Info

Publisher: McGraw-Hill Publishing Company

Published: 2004

International: No

Published: 2004

International: No

A Unified Text That Serves Your Needs. Most colleges offering elementary and intermediate algebra use two different texts, one for each course. As a result, students may be required to purchase two texts; this can result in a considerable amount of topic overlap. Over the last few years, several publishers have issued "combined" texts that take chapters from two texts and merge them into a single book. This has allowed students to purchase a single text, but it has done little to reduce the overlap. The goal of this author team has been to produce a text that was more than a combined text. They wanted to unify the topics and themes of beginning and intermediate algebra in a fluid, non-repetitive text. We also wanted to produce a text that will prepare students from different mathematical backgrounds for college algebra. We believe we have accomplished our goals. For students entering directly from an arithmetic or pre-algebra course, this is a text that contains all of the material needed to prepare for college algebra. It can be offered in two quarters or in two semesters. The new Review Chapter found between chapters 6 and 7 serves as a mid-book review for students preparing to take a final exam that covers the first seven chapters. Finally, we have produced a text that will accommodate those students placing into the second term of a two-term sequence. Here is where the Review Chapter is most valuable. It gives the students an opportunity to check that they have all of the background required to begin in Chapter 7. If the students struggle with any of the material in the Review Chapter, they are referred to the appropriate section for further review.

**New to This Edition **

- A new Review Chapter replaces "Moving to the Intermediate Algebra Level." The Review Chapter provides a concise, comprehensive review of chapters 1 through 6. The chapter contains review exercises and section references.
- Overcoming Math Anxiety Boxes--Located within the first few chapters are suggestions on overcoming math anxiety. These suggestions are designed to be timely and useful, The are the same suggestions most instructors make in class, but sometimes those words are given extra weight when students see them in print.
- The chapter on functions now follows the chapter on polynomials.
- Several new sections have been added to the text:
- Problem Solving with Factoring
- A General Strategy for Factoring
- Rational Functions
- Solving Radical Equations

**Features **

- As the subtitle implies, Hutchison et al. "unifies" elementary algebra and intermediate algebra, reducing repetition that occurs within some combined texts.
- Visualization encouraged through graphing and concrete models.
- Problem solving taught through numerous examples carefully worked out, with a matched "Check Yourself" exercise after each example.

**Hutchison, Donald : Clackamas Community College **

Bergman, Barry : Clackamas Community College

** Hoelzle, Louis : Bucks County Community College **

0 Prealgebra Review

0.1 A Review of Fractions

0.2 Real Numbers

0.3 Adding and Subtracting Real Numbers

0.4 Multiplying and Dividing Real Numbers

0.5 Exponents and Order of Operation

1 From Arithmetic to Algebra

1.1 Transition to Algebra

1.2 Evaluating Algebraic Expressions

1.3 Adding and Subtracting Algebraic Expressions

1.4 Sets

2 Equations and Inequalities

2.1 Solving Equations by Adding and Subtracting

2.2 Solving Equations by Multiplying and Dividing

2.3 Combining the Rules to Solve Equations

2.4 Literal Equations and Their Applications

2.5 Solving Linear Inequalities Using Addition

2.6 Solving Linear Inequalities Using Multiplication

2.7 Solving Absolute Value Equations (Optional)

2.8 Solving Absolute Value Inequalities (Optional)

3 Graphs and Linear Equations

3.1 Solutions of Equations in Two Variables

3.2 The Cartesian Coordinate System

3.3 The Graph of a Linear Equation

3.4 The Slope of a Line

3.5 Forms of Linear Equations

4 Exponents and Polynomials

4.1 Positive Integer Exponents

4.2 Zero and Negative Exponents and Scientific Notation

4.3 Introduction to Polynomials

4.4 Addition and Subtraction of Polynomials

4.5 Multiplication of Polynomials and Special Products

4.6 Division of Polynomials

5 A Beginning Look at Functions

5.1 Relations and Functions

5.2 Tables and Graphs

5.3 Algebra of Functions

5.4 Composition of Functions

6 Factoring Polynomials

6.1 An Introduction to Factoring

6.2 Factoring Special Polynomials

6.3 Factoring Trinomials: The ac method

6.3* Factoring Trinomials: Trial and Error

6.4 Solving Quadratic Equations by Factoring

6.5 Problem Solving with Factoring

6.6 A General Strategy for Factoring

R A Review of Elementary Algebra

R.1 From Arithmetic to Algebra

R.2 Equations and Inequalities

R.3 Graphs and Linear Equations

R.4 Exponents and Polynomials

R.5 A Beginning Look at Functions

R.6 Factoring Polynomials

7 Rational Expressions

7.1 Simplifying Rational Expressions

7.2 Multiplication and Division of Rational Expressions

7.3 Addition and Subtraction of Rational Expressions

7.4 Complex Fractions

7.5 Solving Rational Expressions

7.6 Solving Rational Inequalities

7.7 Rational Functions

8 Systems of Linear Equations and Inequalities

8.1 Solving Systems of Linear Equations by Graphing

8.2 Systems of Equations in Two Variables with Applications

8.3 Systems of Linear Equations in Three Variables

8.4 Matrices (Optional)

8.5 Graphing Linear Inequalities in Two Variables

8.6 Systems of Linear Inequalities in Two Variables

9 Graphical Solutions

9.1 Solving Equations in One Variable Graphically

9.2 Solving Linear Inequalities in One Variable Graphically

9.3 Solving Absolute Value Equations Graphically

9.4 Solving Absolute Value Inequalities Graphically

10 Radicals and Exponents

10.1 Roots and Radicals

10.2 Simplifying Radical Expressions

10.3 Operations on Radical Expressions

10.4 Solving Radical Equations

10.5 Rational Exponents

10.6 Complex Numbers

11 Quadratic Functions

11.1 Solving Quadratic Equations by Completing the Square

11.2 The Quadratic Formula

11.3 Solving Quadratic Equations by Graphing

11.4 Solving Quadratic Inequalities

12 Conic Sections

12.1 More on the Parabola

12.2 The Circle

12.3 Ellipses

12.4 Hyperbolas

13 Exponential and Logarithmic Functions

13.1 Inverse Relations and Functions

13.2 Exponential Functions

13.3 Logarithmic Functions

13.4 Properties of Logarithms

13.5 Logarithmic and Exponential Equations

Appendix A

Appendix A.1 Determinants and Cramer's Rule