# Beginning and Intermediate Algebra

**by**Miller, Julie; O'Neill, Molly; Hyde, Nancy

### 9780073384511

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## Summary

The Miller/O'Neill/Hyde author team continues to offer an enlightened approach grounded in the fundamentals of classroom experience in Beginning and Intermediate Algebra 4e. The text reflects the compassion and insight of its experienced author team with features developed to address the specific needs of developmental level students. Throughout the text, the authors communicate to students the very points their instructors are likely to make during lecture, and this helps to reinforce the concepts and provide instruction that leads students to mastery and success. Also included are Problem Recognition Exercises, designed to help students recognize which solution strategies are most appropriate for a given exercise. These types of exercises, along with the number of practice problems and group activities available, permit instructors to choose from a wealth of problems, allowing ample opportunity for students to practice what they learn in lecture to hone their skills. In this way, the book perfectly complements any learning platform, whether traditional lecture or distance-learning; its instruction is so reflective of what comes from lecture, that students will feel as comfortable outside of class as they do inside class with their instructor.

## Table of Contents

# 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