Intermediate Algebra

With training in mathematics, statistics, and economics, Michael Sullivan III has a varied teaching background that includes 27 years of instruction in both high school and college-level mathematics. He is currently a full-time professor of mathematics at Joliet Junior College. Michael has numerous textbooks in publication, including an Introductory Statistics series and a Precalculus series, which he writes with his father, Michael Sullivan.   Michael believes that his experiences writing texts for college-level math and statistics courses give him a unique perspective as to where students are headed once they leave the developmental mathematics tract. This experience is reflected in the philosophy and presentation of his developmental text series.When not in the classroom or writing, Michael enjoys spending time with his three children, Michael, Kevin, and Marissa, and playing golf. Now that his two sons are getting older, he has the opportunity to do both at the same time!   Kathy Struve has been a classroom teacher for nearly 35 years, first at the high school level and, for the past 27 years, at Columbus State Community College. Kathy embraces classroom diversity: diversity of students’ age, learning styles, and previous learning success. She is aware of the challenges of teaching mathematics at a large, urban community college, where students have varied mathematics backgrounds and may enter college with a high level of mathematics anxiety.   Kathy served as Lead Instructor of the Developmental Algebra sequence at Columbus State, where she developed curriculum, conducted workshops, and provided leadership to adjunct faculty in the mathematics department. She embraces the use of technology in instruction, and has taught web and hybrid classes in addition to traditional face-to-face emporium-style classes. She is always looking for ways to more fully involve students in the learning process. In her spare time Kathy enjoys spending time with her two adult daughters, her four granddaughters, and biking, hiking, and traveling with her husband.   Born and raised in San Diego county, Janet Mazzarella spent her career teaching in culturally and economically diverse high schools before taking a position at Southwestern College 25 years ago. Janet has taught a wide range of mathematics courses from arithmetic through calculus for math/science/engineering majors and has training in mathematics, education, engineering, and accounting.   Janet has worked to incorporate technology into the curriculum by participating in the development of Interactive Math and Math Pro. At Southwestern College, she helped develop the self-paced developmental mathematics program. In addition, Janet was the Dean of the School of Mathematics, Science, and Engineering, the Chair of the Mathematics Department, the faculty union president, and the faculty coordinator for Intermediate Algebra. In the past, free time consisted of racing motorcycles off-road in the Baja 500 and rock climbing, but recently she has given up the adrenaline rush of these activities for the thrill of traveling in Europe. Jessica Bernards and Wendy Fresh of Portland Community College have worked extensively with the author team to create the How to exercises, new Geogebra applet exercises, and have made the assignments for the New MyMathLab courses.

Table of Contents

Preface
R. Review
R.1. Success in Mathematics
R.2. Sets and Classification of Numbers
R.3. Operations on Signed Numbers; Properties of Real Numbers
R.4. Order of Operations
R.5. Algebraic Expressions



Linear Equations and Inequalities

Part I. Linear Equations and Inequalities in One Variable

1.1. Linear Equations in One Variable
1.2. An Introduction to Problem Solving
1.3. Using Formulas to Solve Problems
1.4. Linear Inequalities in One Variable

Putting the Concepts Together (Sections 1.1–1.4)



Part II. Linear Equations and Inequalities in Two Variables

1.5. Rectangular Coordinates and Graphs of Equations
1.6. Linear Equations in Two Variables
1.7. Parallel and Perpendicular Lines
1.8. Linear Inequalities in Two Variables
Chapter 1 Activity: Pass the Paper
Chapter 1 Review
Chapter 1 Test
Cumulative Review Chapters R–1



Relations, Functions, and More Inequalities

2.1. Relations
2.2. An Introduction to Functions
2.3. Functions and Their Graphs

Putting the Concepts Together (Sections 2.1–2.3)


2.4. Linear Functions and Models
2.5. Compound Inequalities
2.6. Absolute Value Equations and Inequalities
Chapter 2 Activity: Shifting Discovery
Chapter 2 Review
Chapter 2 Test


Systems of Linear Equations and Inequalities

3.1. Systems of Linear Equations in Two Variables
3.2. Problem Solving: Systems of Two Linear Equations Containing Two Unknowns
3.3. Systems of Linear Equations in Three Variables

Putting the Concepts Together (Sections 3.1–3.3)


3.4. Using Matrices to Solve Systems
3.5. Determinants and Cramer’s Rule
3.6. Systems of Linear Inequalities
Chapter 3 Activity: Find the Numbers
Chapter 3 Review
Chapter 3 Test
Cumulative Review Chapters R–3
Getting Ready for Chapter 4: Laws of Exponents and Scientific Notation


Polynomials and Polynomial Functions

4.1. Adding and Subtracting Polynomials
4.2. Multiplying Polynomials
4.3. Dividing Polynomials; Synthetic Division

Putting the Concepts Together (Sections 4.1–4.3)


4.4. Greatest Common Factor; Factoring by Grouping
4.5. Factoring Trinomials
4.6. Factoring Special Products
4.7. Factoring: A General Strategy
4.8. Polynomial Equations
Chapter 4 Activity: What Is the Question?
Chapter 4 Review
Chapter 4 Test
Getting Ready for Chapter 5: A Review of Operations on Rational Numbers


Rational Expressions and Rational Functions

5.1. Multiplying and Dividing Rational Expressions
5.2. Adding and Subtracting Rational Expressions
5.3. Complex Rational Expressions

Putting the Concepts Together (Sections 5.1–5.3)


5.4. Rational Equations
5.5. Rational Inequalities
5.6. Models Involving Rational Expressions
5.7. Variation
Chapter 5 Activity: Correct the Quiz
Chapter 5 Review
Chapter 5 Test
Cumulative Review Chapters R–5
Getting Ready for Chapter 6: Square Roots


Radicals and Rational Exponents

6.1. nth Roots and Rational Exponents
6.2. Simplifying Expressions Using the Laws of Exponents
6.3. Simplifying Radical Expressions Using Properties of Radicals
6.4. Adding, Subtracting, and Multiplying Radical Expressions
6.5. Rationalizing Radical Expressions

Putting the Concepts Together (Sections 6.1–6.5)


6.6. Functions Involving Radicals
6.7. Radical Equations and Their Applications
6.8. The Complex Number System
Chapter 6 Activity: Which One Does Not Belong?
Chapter 6 Review
Chapter 6 Test


Quadratic Equations and Functions

7.1. Solving Quadratic Equations by Completing the Square
7.2. Solving Quadratic Equations by the Quadratic Formula
7.3. Solving Equations Quadratic in Form

Putting the Concepts Together (Sections 7.1–7.3)


7.4. Graphing Quadratic Functions Using Transformations
7.5. Graphing Quadratic Functions Using Properties
7.6. Polynomial Inequalities
Chapter 7 Activity: Presidential Decision Making
Chapter 7 Review
Chapter 7 Test
Cumulative Review Chapters R–7


Exponential and Logarithmic Functions

8.1. Composite Functions and Inverse Functions
8.2. Exponential Functions
8.3. Logarithmic Functions

Putting the Concepts Together (Sections 8.1–8.3)


8.4. Properties of Logarithms
8.5. Exponential and Logarithmic Equations
Chapter 8 Activity: Correct the Quiz
Chapter 8 Review
Chapter 8 Test


Conics

9.1. Distance and Midpoint Formulas
9.2. Circles
9.3. Parabolas
9.4. Ellipses
9.5. Hyperbolas

Putting the Concepts Together (Sections 9.1–9.5)


9.6. Systems of Nonlinear Equations
Chapter 9 Activity: How Do You Know That . . . ?
Chapter 9 Review
Chapter 9 Test
Cumulative Review: Chapters R–9


Sequences, Series, and the Binomial Theorem

10.1. Sequences
10.2. Arithmetic Sequences
10.3. Geometric Sequences and Series

Putting the Concepts Together (Sections 10.1–10.3)


10.4. The Binomial Theorem
Chapter 10 Activity: Discover the Relation
Chapter 10 Review
Chapter 10 Test



Answers to Selected Exercises Applications Index Subject Index Photo Credits