# Beginning and Intermediate Algebra

4^{th}Edition

ISBN10: 0073384518

ISBN13: 9780073384511

Copyright: 2014

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### Program Details

# Beginning and Intermediate Algebra 4e

### Chapter 1: Set of Real Numbers

#### 1.1 Fractions

#### 1.2 Introduction to Algebra and the Set of Real Numbers

#### 1.3 Exponents, Square Roots, and Order of Operations

#### 1.4 Addition of Real Numbers

#### 1.5 Subtraction of Real Numbers

Problem Recognition Exercises—Addition and Subtraction of Real Numbers

#### 1.6 Multiplication and Division of Real Numbers

Problem Recognition Exercises—Adding, Subtracting, Multiplying and Dividing Real Numbers

#### 1.7 Properties of Real Numbers and Simplifying Expressions

### Chapter 2: Linear Equations and Inequalities

#### 2.1 Addition, Subtraction, Multiplication, and Division Properties of Equality

#### 2.2 Solving Linear Equations

#### 2.3 Linear Equations: Clearing Fractions and Decimals

Problem Recognition Exercises—Equations vs.Expressions

#### 2.4 Applications of Linear Equations: Introduction to Problem Solving

#### 2.5 Applications Involving Percents

#### 2.6 Formulas and Applications of Geometry

#### 2.7 Mixture Applications and Uniform Motion

#### 2.8 Linear Inequalities

### Chapter 3: Graphing Linear Equations in Two Variables

#### 3.1 Rectangular Coordinate System

#### 3.2 Linear Equations in Two Variables

#### 3.3 Slope of a Line and Rate of Change

#### 3.4 Slope-Intercept Form of a Linear Equation

Problem Recognition Exercises-Linear Equations in Two Variables

#### Point-Slope Formula

#### Applications of Linear Equations

### Chapter 4: Systems of Linear Equations

#### 4.1 Solving Systems of Equations by the Graphing Method

#### 4.2 Solving Systems of Equations by the Substitution Method

#### 4.3 Solving Systems of Equations by the Addition Method

Problem Recognition Exercises: Systems of Equations

#### 4.4 Applications of Linear Equations in Three Variables

#### 4.5 Systems of Linear Equations in Three Variables

#### 4.6 Applications of Systems of Linear Equations in Three Variables

### Chapter 5: Polynomials and Properties of Exponents

#### 5.1 Multiplying and Dividing Expressions with Common Bases

#### 5.2 More Properties of Exponents

#### 5.3 Definitions of b^0 and b^-n

Problem Recognition Exercises-Properties of Exponents

#### 5.4 Scientific Notation

#### 5.5 Addition and Subtraction of Polynomials

#### 5.6 Multiplication of Polynomials

#### 5.7 Division of Polynomials

Problem Recognition Exercises-Operations on Polynomials

### Chapter 6: Factoring Polynomials

#### 6.1 Greatest Common Factor and Factoring by Grouping

#### 6.2 Factoring Trinomials of the Form x^2 + bx + c

#### 6.3 Factoring Trinomials: Trial-and-Error Method

#### 6.4 Factoring Trinomials: AC-Method

#### 6.5 Difference of Squares and Perfect Square Trinomials

#### 6.6 Sum and Difference of Cubes

Problem Recognition Exercises-Factoring Strategy

#### 6.7 Solving Equations Using the Zero Product Rule

Problem Recognition Exercises-Polynomial Expressions and Polynomial Equations

#### 6.8 Applications of Quadratic Equations

### Chapter 7: Rational Expressions and Equations

#### 7.1 Introduction of Rational Expressions

#### 7.2 Multiplication and Division of Rational Expressions

#### 7.3 Least Common Denominator

#### 7.4 Addition and Subtraction of Rational Expressions

Problem Recognition Exercises-Operations of Rational Expressions

#### 7.5 Complex Fractions

#### 7.6 Rational Equations

Problem Recognition Exercises-Comparing Rational Equations and Rational Expressions

#### 7.7 Applications of Rational Equations and Proportions

### Chapter 8: Relations and Functions

#### 8.1 Introduction of Relations

#### 8.2 Introduction of Functions

#### 8.3 Graphs of Functions

Problem Recognition Exercises: Characteristics of Relations

#### 8.4 Alebra of Functions and Composition

#### 8.5 Variation

### Chapter 9: More Equations and Inequalities

#### 9.1 Compound Inequalities

#### 9.2 Polynomial and Rational Enequalities

#### 9.3 Absolute Value Equations

#### 9.4 Absolute Value Inequalities

Problem Recognition Exercises: Equations and Inequalities

#### 9.5 Linear and Compound Inequalities in Two Variables

### Chapter 10: Radicals and Complex Numbers

#### 10.1 Definition of an nth Root

#### 10.2 Rational Exponents

#### 10.3 Simplifying Radical Expressions

#### 10.4 Addition and Subtraction of Radicals

#### 10.5 Multiplication of Radical

Problem Recognition Exercises: Simplifying Radical Expressions

#### 10.6 Division of Radicals and Rationalization

#### 10.7 Solving Radical Equations

#### 10.8 Complex Numbers

### Chapter 11: Quadratic Equations, Functions and Inequalities

#### 11.1 Square Root Property and Completing the Square

#### 11.2 Quadratic Formula

#### 11.3 Equations in Quadratic Form

Problem Recognition Exercises: Quadratic and Quadratic Type Equations

#### 11.4 Graphs of Quadratic Functions

#### 11.5 Vertex of a Parabola: Applications and Modeling

### Chapter 12: Exponential and Logarithmic Functions and Applications

#### 12.1 Inverse Functions

#### 12.2 Exponential Functions

#### 12.3 Logarithmic Functions

Problem Recognition Exercises: Logarithmic and Exponential Forms

#### 12.4 Properties of Logarithms

#### 12.5 The Irrational Number and change of Base

#### 12.6 Logarithmic and Exponential Equations and Applications

### Chapter 13: Conic Sections

#### 13.1 Distance Formula, Midpoint Formula, and Circles

#### 13.2 More on the Parabola

#### 13.3 The Ellipse and Hyperbola

Problem Recognition Exercises: Formulas and Conic Sections

#### 13.4 Nonlinear Systems of Equation in Two Variables

#### 13.5 Nonlinear Inequalities and Systems of Inequalities

### Chapter 14: Binomial Expansions, Sequences, and Series

#### 14.1 Binomial Expansions

#### 14.2 Sequences and Series

#### 14.3 Arithmetic Sequences and Series

#### 14.4 Geometric Sequences and Series

Problem Recognition Exercises: Identifying Arithmetic and Geometric Series

### Additional Topics Appendix

#### A.1 Mean, Median, and Mode

#### A.2 Introduction to Geometry

#### A.3 Solving Systems of Linear Equations Using Matrices

#### A.4 Determinants and Cramer’s Rule

# About the Author

**Julie Miller**

Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers.

**My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I can remember using graph paper to plot data points for his experiments and doing simple calculations. He would then tell me what the peaks and features in the graph meant in the context of his experiment. I think that applications and hands-on experience made math come alive for me and I’d like to see math come alive for my students.**

**Molly O'Neill**

Molly ONeill is from Daytona State College, where she has taught for 22 years in the School of Mathematics. She has taught a variety of courses from developmental mathematics to calculus. Before she came to Florida, Molly taught as an adjunct instructor at the University of Michigan-Dearborn, Eastern Michigan University, Wayne State University, and Oakland Community College. Molly earned a bachelor of science in mathematics and a master of arts and teaching from Western Michigan University in Kalamazoo, Michigan. Besides this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus and has reviewed texts for developmental mathematics.

**I differ from many of my colleagues in that math was not always easy for me. But in seventh grade I had a teacher who taught me that if I follow the rules of mathematics, even I could solve math problems. Once I understood this, I enjoyed math to the point of choosing it for my career. I now have the greatest job because I get to do math every day and I have the opportunity to influence my students just as I was influenced. Authoring these texts has given me another avenue to reach even more students.**

**Nancy Hyde**

Nancy Hyde served as a full-time faculty member of the Mathematics Department at Broward College for 24 years. During this time she taught the full spectrum of courses from developmental math through differential equations. She received a bachelor of science degree in math education from Florida State University and a master’s degree in math education from Florida Atlantic University. She has conducted workshops and seminars for both students and teachers on the use of technology in the classroom. In addition to this textbook, she has authored a graphing calculator supplement for College Algebra.

**I grew up in Brevard County, Florida, where my father worked at Cape Canaveral. I was always excited by mathematics and physics in relation to the space program. As I studied higher levels of mathematics I became more intrigued by its abstract nature and infinite possibilities. It is enjoyable and rewarding to convey this perspective to students while helping them to understand mathematics.**

# Beginning and Intermediate Algebra 4e

### Chapter 1: Set of Real Numbers

#### 1.1 Fractions

#### 1.2 Introduction to Algebra and the Set of Real Numbers

#### 1.3 Exponents, Square Roots, and Order of Operations

#### 1.4 Addition of Real Numbers

#### 1.5 Subtraction of Real Numbers

Problem Recognition Exercises—Addition and Subtraction of Real Numbers

#### 1.6 Multiplication and Division of Real Numbers

Problem Recognition Exercises—Adding, Subtracting, Multiplying and Dividing Real Numbers

#### 1.7 Properties of Real Numbers and Simplifying Expressions

### Chapter 2: Linear Equations and Inequalities

#### 2.1 Addition, Subtraction, Multiplication, and Division Properties of Equality

#### 2.2 Solving Linear Equations

#### 2.3 Linear Equations: Clearing Fractions and Decimals

Problem Recognition Exercises—Equations vs.Expressions

#### 2.4 Applications of Linear Equations: Introduction to Problem Solving

#### 2.5 Applications Involving Percents

#### 2.6 Formulas and Applications of Geometry

#### 2.7 Mixture Applications and Uniform Motion

#### 2.8 Linear Inequalities

### Chapter 3: Graphing Linear Equations in Two Variables

#### 3.1 Rectangular Coordinate System

#### 3.2 Linear Equations in Two Variables

#### 3.3 Slope of a Line and Rate of Change

#### 3.4 Slope-Intercept Form of a Linear Equation

Problem Recognition Exercises-Linear Equations in Two Variables

#### Point-Slope Formula

#### Applications of Linear Equations

### Chapter 4: Systems of Linear Equations

#### 4.1 Solving Systems of Equations by the Graphing Method

#### 4.2 Solving Systems of Equations by the Substitution Method

#### 4.3 Solving Systems of Equations by the Addition Method

Problem Recognition Exercises: Systems of Equations

#### 4.4 Applications of Linear Equations in Three Variables

#### 4.5 Systems of Linear Equations in Three Variables

#### 4.6 Applications of Systems of Linear Equations in Three Variables

### Chapter 5: Polynomials and Properties of Exponents

#### 5.1 Multiplying and Dividing Expressions with Common Bases

#### 5.2 More Properties of Exponents

#### 5.3 Definitions of b^0 and b^-n

Problem Recognition Exercises-Properties of Exponents

#### 5.4 Scientific Notation

#### 5.5 Addition and Subtraction of Polynomials

#### 5.6 Multiplication of Polynomials

#### 5.7 Division of Polynomials

Problem Recognition Exercises-Operations on Polynomials

### Chapter 6: Factoring Polynomials

#### 6.1 Greatest Common Factor and Factoring by Grouping

#### 6.2 Factoring Trinomials of the Form x^2 + bx + c

#### 6.3 Factoring Trinomials: Trial-and-Error Method

#### 6.4 Factoring Trinomials: AC-Method

#### 6.5 Difference of Squares and Perfect Square Trinomials

#### 6.6 Sum and Difference of Cubes

Problem Recognition Exercises-Factoring Strategy

#### 6.7 Solving Equations Using the Zero Product Rule

Problem Recognition Exercises-Polynomial Expressions and Polynomial Equations

#### 6.8 Applications of Quadratic Equations

### Chapter 7: Rational Expressions and Equations

#### 7.1 Introduction of Rational Expressions

#### 7.2 Multiplication and Division of Rational Expressions

#### 7.3 Least Common Denominator

#### 7.4 Addition and Subtraction of Rational Expressions

Problem Recognition Exercises-Operations of Rational Expressions

#### 7.5 Complex Fractions

#### 7.6 Rational Equations

Problem Recognition Exercises-Comparing Rational Equations and Rational Expressions

#### 7.7 Applications of Rational Equations and Proportions

### Chapter 8: Relations and Functions

#### 8.1 Introduction of Relations

#### 8.2 Introduction of Functions

#### 8.3 Graphs of Functions

Problem Recognition Exercises: Characteristics of Relations

#### 8.4 Alebra of Functions and Composition

#### 8.5 Variation

### Chapter 9: More Equations and Inequalities

#### 9.1 Compound Inequalities

#### 9.2 Polynomial and Rational Enequalities

#### 9.3 Absolute Value Equations

#### 9.4 Absolute Value Inequalities

Problem Recognition Exercises: Equations and Inequalities

#### 9.5 Linear and Compound Inequalities in Two Variables

### Chapter 10: Radicals and Complex Numbers

#### 10.1 Definition of an nth Root

#### 10.2 Rational Exponents

#### 10.3 Simplifying Radical Expressions

#### 10.4 Addition and Subtraction of Radicals

#### 10.5 Multiplication of Radical

Problem Recognition Exercises: Simplifying Radical Expressions

#### 10.6 Division of Radicals and Rationalization

#### 10.7 Solving Radical Equations

#### 10.8 Complex Numbers

### Chapter 11: Quadratic Equations, Functions and Inequalities

#### 11.1 Square Root Property and Completing the Square

#### 11.2 Quadratic Formula

#### 11.3 Equations in Quadratic Form

Problem Recognition Exercises: Quadratic and Quadratic Type Equations

#### 11.4 Graphs of Quadratic Functions

#### 11.5 Vertex of a Parabola: Applications and Modeling

### Chapter 12: Exponential and Logarithmic Functions and Applications

#### 12.1 Inverse Functions

#### 12.2 Exponential Functions

#### 12.3 Logarithmic Functions

Problem Recognition Exercises: Logarithmic and Exponential Forms

#### 12.4 Properties of Logarithms

#### 12.5 The Irrational Number and change of Base

#### 12.6 Logarithmic and Exponential Equations and Applications

### Chapter 13: Conic Sections

#### 13.1 Distance Formula, Midpoint Formula, and Circles

#### 13.2 More on the Parabola

#### 13.3 The Ellipse and Hyperbola

Problem Recognition Exercises: Formulas and Conic Sections

#### 13.4 Nonlinear Systems of Equation in Two Variables

#### 13.5 Nonlinear Inequalities and Systems of Inequalities

### Chapter 14: Binomial Expansions, Sequences, and Series

#### 14.1 Binomial Expansions

#### 14.2 Sequences and Series

#### 14.3 Arithmetic Sequences and Series

#### 14.4 Geometric Sequences and Series

Problem Recognition Exercises: Identifying Arithmetic and Geometric Series

### Additional Topics Appendix

#### A.1 Mean, Median, and Mode

#### A.2 Introduction to Geometry

#### A.3 Solving Systems of Linear Equations Using Matrices

#### A.4 Determinants and Cramer’s Rule

# About the Author

**Julie Miller**

Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers.

**My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I can remember using graph paper to plot data points for his experiments and doing simple calculations. He would then tell me what the peaks and features in the graph meant in the context of his experiment. I think that applications and hands-on experience made math come alive for me and I’d like to see math come alive for my students.**

**Molly O'Neill**

Molly ONeill is from Daytona State College, where she has taught for 22 years in the School of Mathematics. She has taught a variety of courses from developmental mathematics to calculus. Before she came to Florida, Molly taught as an adjunct instructor at the University of Michigan-Dearborn, Eastern Michigan University, Wayne State University, and Oakland Community College. Molly earned a bachelor of science in mathematics and a master of arts and teaching from Western Michigan University in Kalamazoo, Michigan. Besides this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus and has reviewed texts for developmental mathematics.

**I differ from many of my colleagues in that math was not always easy for me. But in seventh grade I had a teacher who taught me that if I follow the rules of mathematics, even I could solve math problems. Once I understood this, I enjoyed math to the point of choosing it for my career. I now have the greatest job because I get to do math every day and I have the opportunity to influence my students just as I was influenced. Authoring these texts has given me another avenue to reach even more students.**

**Nancy Hyde**

Nancy Hyde served as a full-time faculty member of the Mathematics Department at Broward College for 24 years. During this time she taught the full spectrum of courses from developmental math through differential equations. She received a bachelor of science degree in math education from Florida State University and a master’s degree in math education from Florida Atlantic University. She has conducted workshops and seminars for both students and teachers on the use of technology in the classroom. In addition to this textbook, she has authored a graphing calculator supplement for College Algebra.

**I grew up in Brevard County, Florida, where my father worked at Cape Canaveral. I was always excited by mathematics and physics in relation to the space program. As I studied higher levels of mathematics I became more intrigued by its abstract nature and infinite possibilities. It is enjoyable and rewarding to convey this perspective to students while helping them to understand mathematics.**

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