Intermediate Algebra

Barbara Johnson has a BS in mathematics from Bob Jones University and a MS in mathematics from Clemson University, and she is currently pursuing a PhD in Educational Studies at Ball state University. She has taught high school and college math for 30 years, and she enjoys the challenge of helping each student grow in appreciation for and understanding of mathematics. As a Purdue Master Gardener, she also enjoys helping others learn gardening skills. Believing that the best teacher is always learning, she is also a student of karate.Marvin Bittinger has taught math at the university level for more than thirty-eight years, and he is now professor emeritus of mathematics education at Indiana University-Purdue University. Professor Bittinger has authored numerous textbooks on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.David Ellenbogen has taught math at the college level for nearly 30 years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has taught at St. Michael's College and The University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two Year Colleges (AMATYC) since 1985, having served on its Developmental Mathematics Committee and as a delegate. He has been a member of the Mathematical Association of America (MAA) since 1979. He has authored dozens of texts on topics ranging from prealgebra to calculus and has delivered lectures on the use of language in mathematics. Professor Ellenbogen received his bachelor's degree in mathematics from Bates College and his master’s degree in community college mathematics education from The University of Massachusetts–Amherst. In his spare time, he enjoys playing piano, biking, hiking, skiing, and volunteer work. He currently serves on the boards of the Vermont Sierra Club and the Vermont Bicycle Pedestrian Coalition. He has two sons, Monroe and Zachary.

• Table of Contents Algebra and Problem Solving 1.1 Some Basics of Algebra1.2 Operations and Properties of Real Numbers1.3 Solving Equations1.4 Introduction to Problem Solving1.5 Formulas, Models, and Geometry1.6 Properties of Exponents1.7 Scientific NotationGraphs, Functions, and Linear Equations 2.1 Graphs2.2 Functions2.3 Linear Functions: Slope, Graphs, and Models2.4 Another Look at Linear Graphs2.5 Equations of Lines and Modeling2.6 The Algebra of FunctionsSystems of Linear Equations and Problem Solving 3.1 Systems of Equations in Two Variables3.2 Solving by Substitution or Elimination3.3 Solving Applications: Systems of Two Equations3.4 Systems of Equations in Three Variables3.5 Solving Applications: Systems of Three Equations3.6 Elimination Using Matrices3.7 Determinants and Cramer’S Rule3.8 Business and Economics ApplicationsInequalities and Problem Solving 4.1 Inequalities and Applications4.2 Intersections, Unions, and Compound Inequalities4.3 Absolute-Value Equations and Inequalities4.4 Inequalities in Two Variables4.5 Applications Using Linear ProgrammingPolynomials and Polynomial Functions 5.1 Introduction to Polynomials and Polynomial Functions5.2 Multiplication of Polynomials5.3 Common Factors and Factoring by Grouping5.4 Factoring Trinomials5.5 Factoring Perfect-Square Trinomials and Differences of Squares5.6 Factoring Sums or Differences of Cubes5.7 Factoring: A General Strategy5.8 Applications of Polynomial EquationsRational Expressions, Equations, and Functions 6.1 Rational Expressions and Functions: Multiplying and Dividing6.2 Rational Expressions and Functions: Adding and Subtracting6.3 Complex Rational Expressions6.4 Rational Equations6.5 Solving Applications Using Rational Equations6.6 Division of Polynomials6.7 Synthetic Division and the Remainder Theorem6.8 Formulas, Applications, and VariationExponents and Radicals 7.1 Radical Expressions and Functions7.2 Rational Numbers as Exponents7.3 Multiplying Radical Expressions7.4 Dividing Radical Expressions7.5 Expressions Containing Several Radical Terms7.6 Solving Radical Equations7.7 The Distance Formula, the Midpoint Formula, and Other Applications7.8 The Complex NumbersQuadratic Functions and Equations 8.1 Quadratic Equations8.2 The Quadratic Formula8.3 Studying Solutions of Quadratic Equations8.4 Applications Involving Quadratic Equations8.5 Equations Reducible to Quadratic8.6 Quadratic Functions and Their Graphs8.7 More About Graphing Quadratic Functions8.8 Problem Solving and Quadratic Functions8.9 Polynomial Inequalities and Rational InequalitiesExponential Functions and Logarithmic Functions 9.1 Composite Functions and Inverse Functions9.2 Exponential Functions9.3 Logarithmic Functions9.4 Properties of Logarithmic Functions9.5 Common Logarithms and Natural Logarithms9.6 Solving Exponential Equations and Logarithmic Equations9.7 Applications of Exponential Functions and Logarithmic FunctionsConic Sections 10.1 Conic Sections: Parabolas and Circles10.2 Conic Sections: Ellipses10.3 Conic Sections: Hyperbolas10.4 Nonlinear Systems of EquationsSequences, Series, and the Binomial Theorem 11.1 Sequences and Series11.2 Arithmetic Sequences and Series11.3 Geometric Sequences and Series11.4 The Binomial Theorem