Introduction 1 What You''ll Find 1 How This Workbook Is Organized 2 Part 1: Questions 2 Part 2: Answers 3 Beyond the Book 3 Where to Go for Additional Help 4 Part 1: The Questions 5 Chapter 1: Signing on with Signed Numbers 7 The Problems You''ll Work On 7 What to Watch Out For 7 Placing Real Numbers on the Number Line 8 Using the Absolute Value Operation 8 Adding Signed Numbers 8 Subtracting Signed Numbers 9 Multiplying and Dividing Signed Numbers 10 Chapter 2: Recognizing Algebraic Properties and Notation 13 The Problems You''ll Work On 13 What to Watch Out For 13 Applying Traditional Grouping Symbols 14 Introducing Some Non-Traditional Grouping Symbols 14 Distributing Multiplication over Addition and Subtraction 15 Associating Terms Differently with the Associative Property 15 Rearranging with the Commutative Property 16 Applying More Than One Property to an Expression 16 Chapter 3: Working with Fractions and Decimals 17 The Problems You''ll Work On 17 What to Watch Out For 18 Adding and Subtracting Fractions 18 Multiplying Fractions 18 Dividing Fractions 18 Simplifying Complex Fractions 19 Adding and Subtracting Decimals 19 Multiplying Decimals 20 Dividing Decimals 20 Changing Fractions to Decimals 20 Changing Decimals to Fractions 21 Chapter 4: Making Exponential Expressions and Operations More Compatible 23 The Problems You''ll Work On 23 What to Watch Out For 23 Multiplying and Dividing Exponentials with the Same Base 24 Raising a Power to a Power 24 Combining Different Operations on Exponentials 25 Changing the Base to Perform an Operation 26 Working with Scientific Notation 26 Chapter 5: Raking in Radicals 29 The Problems You''ll Work On 29 What to Watch Out For 29 Simplifying Radical Expressions 30 Rationalizing Denominators 30 Using Fractional Exponents for Radicals 31 Evaluating Expressions with Fractional Exponents 32 Operating on Radicals 32 Operating on Factors with Fractional Exponents 33 Estimating Values of Radicals 33 Chapter 6: Creating More User-Friendly Algebraic Expressions 35 The Problems You''ll Work On 35 What to Watch Out For 35 Adding and Subtracting Like Terms 36 Multiplying and Dividing Factors 36 Simplifying Expressions Using the Order of Operations 37 Evaluating Expressions Using the Order of Operations 38 Operating with Factorials 38 Focusing on Function Notation 39 Chapter 7: Multiplying by One or More Terms 41 The Problems You''ll Work On 41 What to Watch Out For 41 Distributing One Term Over Sums and Differences 42 Distributing Using Division 42 Multiplying Binomials Using Distributing 42 Multiplying Binomials Using FOIL 43 Distributing Binomials Over Trinomials 43 Squaring Binomials 44 Raising Binomials to the Third Power 44 Using Pascal''s Triangle 44 Finding Special Products of Binomials and Trinomials 45 Chapter 8: Dividing Algebraic Expressions 47 The Problems You''ll Work On 47 What to Watch Out For 47 Dividing with Monomial Divisors 48 Monomial Divisors and Remainders 48 Using Long Division to Divide with Binomials 49 Dividing with Binomials Using Synthetic Division 50 Dividing with Higher Power Divisors 50 Chapter 9: Factoring Basics 53 The Problems You''ll Work On 53 What to Watch Out For 53 Finding Divisors Using Rules of Divisibility 54 Writing Prime Factorizations 54 Factoring Out a GCF 55 Reducing Fractions with a Common GCF 56 Chapter 10: Factoring Binomials 57 The Problems You''ll Work On 57 What to Watch Out For 57 Factoring the Difference of Perfect Squares 58 Factoring the Sum or Difference of Two Perfect Cubes 58 Factoring More Than Once 59 Chapter 11: Factoring Quadratic Trinomials 61 The Problems You''ll Work On 61 What to Watch Out For 61 Factoring Out the GCF of a Trinomial 62 Factoring Trinomials into the Products of Binomials 62 Factoring Quadratic-Like Expressions 63 Factoring Completely Using More Than One Technique 63 Chapter 12: Other Factoring Techniques 65 The Problems You''ll Work On 65 What to Watch Out For 65 Factoring by Grouping 66 Combining Other Factoring Techniques with Grouping 66 Using Multiple Factoring Methods 66 Chapter 13: Solving Linear Equations 69 The Problems You''ll Work On 69 What to Watch Out For 69 Solving Linear Equations Using Basic Operations 70 Dealing with Fractions in Linear Equations 71 Chapter 14: Taking on Quadratic Equations 73 The Problems You''ll Work On 73 What to Watch Out For 73 Applying the Square Root Rule to Quadratic Equations 74 Solving Quadratic Equations Using Factoring 74 Applying the Quadratic Formula to Quadratic Equations 75 Completing the Square to Solve Quadratic Equations 76 Writing Complex Numbers in the Standard a + bi Form 76 Finding Complex Solutions Using the Quadratic Formula 77 Chapter 15: Solving Polynomials with Powers Three and Higher 79 The Problems You''ll Work On 79 What to Watch Out For 79 Applying Descartes''s Rule of Signs to Count Real Roots 80 Applying the Rational Root Theorem to List Roots 80 Determining Whether Numbers Are Roots 81 Solving for the Roots of Polynomials 81 Chapter 16: Reining in Radical and Absolute Value Equations 83 The Problems You''ll Work On 83 What to Watch Out For 83 Solving Basic Radical Equations 84 Checking for Extraneous Roots 84 Squaring Both Sides of Equations Twice 85 Solving Radicals with Roots Other Than Square Roots 85 Solving Absolute Value Equations 85 Handling Absolute Value Equations with No Solution 86 Chapter 17: Making Inequalities More Fair 87 The Problems You''ll Work On 87 What to Watch Out For 87 Performing Operations on Inequalities 88 Writing Inequalities Using Interval Notation 88 Changing Interval Notation to Inequality Notation 88 Solving Linear Inequalities 89 Taking on Compound Inequalities 89 Solving Quadratic Inequalities 89 Finding Solutions of Nonlinear Inequalities 90 Rewriting and Solving Absolute Value Inequalities 91 Delving into Complex Inequalities 91 Chapter 18: Using Established Formulas 93 The Problems You''ll Work On 93 What to Watch Out For 93 Getting Interested in Interest Problems 94 Heating It Up with Temperature Problems 94 Adding up Natural Numbers 95 Going the Distance with the Distance Formula 95 Getting the Inside Scoop with Sums of Interior Angles 96 Averaging Out the Numbers 97 Summing the Squares of Numbers 97 Finding the Terms of a Sequence 97 Adding the Terms in an Arithmetic Sequence 98 Using the Formula for the Sum of Cubes 98 Compounding the Problems Involving Compound Interest 98 Chapter 19: Using Formulas in Geometric Story Problems 101 The Problems You''ll Work On 101 What to Watch Out For 102 Working around the Perimeter of Rectangles 102 Using the Area Formula for a Trapezoid 103 Tackling Area and Perimeter of a Square 103 Solving Problems Using the Perimeter of a Triangle 103 Working with the Area and Perimeter of a Rectangle 104 Using the Formula for the Area of a Hexagon 104 Getting Pythagoras Involved in the Area of a Triangle 104 Making Use of the Volume of a Box 105 Working with the Volume of a Cylinder 105 Changing Radians to Degrees and Degrees to Radians 105 Determining the Height of an Object 106 Working with Heron''s Formula for the Area of a Triangle 106 Chapter 20: Tackling Traditional Story Problems 107 The Problems You''ll Work On 107 What to Watch Out For 107 Tackling Age Problems 108 Working with Consecutive Integers 109 Getting the Job Done on Work Problems 110 Counting on Quality and Quantity Problems 111 Solving Money Problems 111 Chapter 21: Graphing Basics 113 The Problems You''ll Work On 113 What to Watch Out For 113 Plotting Points on the Coordinate System 114 Determining the Quadrant of a Point 115 Finding the Intercepts of a Line 115 Calculating the Slope of a Line from Two Points 116 Determining a Line''s Slope from Its Equation 117 Sketching the Graph of a Line from Its Equation 117 Sketching Lines Using Two Points 118 Chapter 22: Using the Algebra of Lines 119 The Problems You''ll Work On 119 What to Watch Out For 119 Writing Equations of Lines Using the Slope and a Point 120 Writing the Equation of a Line Using Two Points 120 Dealing with Slopes of Parallel and Perpendicular Lines 121 Finding Equations of Lines Parallel or Perpendicular to One Given 121 Computing the Distance Between Points.