Algebra for College Students

PrefaceAcknowledgmentsTo the StudentChapter One the REAL Number System 1.1 The Real Number System 1.2 Arithmetic Operations: Fractions 1.3 Algebraic Expressions 1.4 Operating with Signed Numbers 1.5 Properties of Real Numbers 1.6 Absolute Value and InequalitiesChapter Two Polynomials 2.1 Polynomials 2.2 Addition and Subtraction of Polynomials 2.3 Multiplication of Polynomials 2.4 Factoring 2.5 Special FactorsChapter Three Linear Equations and Inequalities 3.1 Linear Equations in One Variable 3.2 Applications 3.3 Linear Inequalities 3.4 Absolute Value in Equations and InequalitiesChapter Four Word Problems 4.1 From Words to Algebra 4.2 Coin Problems 4.3 Investment Problems 4.4 Distance (Uniform Motion) Problems 4.5 Mixture ProblemsChapter Five Algebraic Fractions 5.1 Multiplication and Division of Fractions 5.2 Addition and Subtraction of Fractions 5.3 Complex Fractions 5.4 Ratio and Proportion 5.5 Equations and Inequalities with Fractions 5.6 Applications; Work ProblemsChapter Six Functions 6.1 Rectangular Coordinate Systems 6.2 Functions and Function Notation 6.3 Graphs of Functions 6.4 Increasing and Decreasing Functions 6.5 Direct and Inverse VariationChapter Seven the Straight Line 7.1 Slope of the Straight Line 7.2 Equations of the Straight Line 7.3 Further Properties of the Straight Line 7.4 Linear Inequalities in Two VariablesChapter Eight Exponents, Radicals, and Complex Numbers 8.1 Positive Integer Exponents 8.2 Integer Exponents 8.3 Rational Exponents and Radicals 8.4 Evaluating and Simplifying Radicals 8.5 Operations with Radicals 8.6 Complex NumbersChapter Nine Second-Degree Equations and Inequalities 9.1 Solving Quadratic Equations 9.2 The Quadratic Formula 9.3 Roots of a Quadratic Equation: The Discriminant 9.4 Applications 9.5 Forms Leading to Quadratics 9.6 Second-Degree InequalitiesChapter Ten Roots of Polynomials 10.1 Polynomial Division and Synthetic Division 10.2 The Remainder and Factor Theorems 10.3 Factors and Roots 10.4 Real and Rational RootsChapter Eleven Exponential and Logarithmic Functions 11.1 Combining Functions; Inverse Functions 11.2 Exponential Functions 11.3 Logarithmic Functions 11.4 Properties of Logarithms 11.5 Computing with Logarithms 11.6 Exponential and Logarithmic EquationsChapter Twelve Analytic Geometry: The Conic Sections 12.1 Distance and Midpoint Formulas 12.2 Symmetry 12.3 The Circle 12.4 The Parabola 12.5 The Ellipse and Hyperbola 12.6 Identifying the Conic Sections Chapter Thirteen Systems of Equations 13.1 Systems of Linear Equations 13.2 Solving by Elimination 13.3 Applications 13.4 Systems of Linear Equations in Three Unknowns 13.5 Systems Involving Nonlinear EquationsChapter Fourteen Matrices and Determinants 14.1 Matrices and Linear Systems 14.2 Determinants 14.3 Cramer's RuleChapter Fifteen Topics in Algebra 15.1 Arithmetic Progressions 15.2 Geometric Progressions 15.3 The Binomial Theorem 15.4 Counting: Permutations and CombinationsAppendix/TablesAnswers to Odd-Numbered Exercises and Progress TestsIndex