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B A S I C

ALGEBRA I T I O N

SAUNDERS COLLEGE PUBLISHING Harcour t Brace College Publ i shers

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Contents

Review of Ari thmetic 1

CHAPTER R PRETEST 3

R.1 Review: Positive Rational Numbers 5 R.2 Review: Addition and Subtraction of

Positive Rational Numbers 13 R.3 Review: Multiplication and Division of

Positive Rational Numbers 19 R.4 Review: Percents 31

CHAPTER R POST-TEST 37

The Language of Algebra and Signed Numbers 39

CHAPTER 1 PRE-TEST 41

1.1 Whole Number Exponents 43 1.2 Order of Operations and Evaluating

Expressions 53 1.3 The Language of Algebra 63 1.4 Signed Numbers, Opposites, and Absolute

Value 79 1.5 Adding Signed Numbers 89 1.6 Subtracting Signed Numbers 101 1.7 Multiplying Signed Numbers- 111 1.8 Dividing Signed Numbers 123 1.9 Order of Operations: A Review 133

CHAPTER 1

CHAPTER 1

TRUE-FALSE CONCEPT REVIEW 145 POST-TEST 147

Linear Equat ions, Inequali t ies, and Exponents 149

CHAPTER 2 PRETEST 151

2.1 Equations of the Form x + a = b or x — a = b 153

2.2 Equations of the Form ax = b or

2.3 2.4

2.5 2.6 2.7 2.8

— = b 163 a Solving Percent Problems 177 Equations of the Form ax + b = c,

x u c, or b = c ax x

c, — + b a

189

201 Writing and Graphing Inequalities Solving Inequalities 211 Three Laws of Exponents 223 Integer Exponents and the Fourth and Fifth Laws of Exponents 235 Scientific Notation 247 2.9

CHAPTER 2 TRUE-FALSE CONCEPT REVIEW 255

CHAPTER 2 POST-TEST 257

Algebra of Polynomials 259


263 3.1 Introduction to Polynomials 3.2 Adding Polynomials 271 3.3 Subtracting Polynomials 285 3.4 Application Solutions 297 3.5 Multiplying Polynomials 305 3.6 Multiplying Binomials 319 3.7 Special Binomial Products 329 3.8 Dividing Polynomials 339

CHAPTER 3

CHAPTER 3


Factor ing Polynomials 353


4.1 Solving Equations of the Form A • B = 0 357

xxi i

CONTENTS xxiii

4.2 Factoring Polynomials: Monomial Factors 367

4.3 Factoring Polynomials: Factoring by Grouping 377

4.4 Factoring Trinomials of the Form x2 + bx + c 385

4.5 Factoring: Special Cases 397 4.6 Factoring Trinomials of the Form

ax2 + bx + c 411 4.7 Factoring Polynomials: A Review 423



Fractions of Algebra 437


5.1 Multiplying and Dividing, Par t 1 5.2 Reducing and Building 453 5.3 Multiplying and Dividing, Par t 2 5.4 Adding and Subtracting, Par t 1 5.5 Least Common Multiple 501 5.6 Adding and Subtracting, Par t 2 5.7 Complex Fractions 525 5.8 Ratio and Proportion 537 5.9 Variation 549

441

467 483

515

CHAPTER 5

CHAPTER 5


Square Roots and Related Equations 567


6.1 Square Roots 569 6.2 Simplifying Radicals 581 6.3 Multiplying Radicals 591 6.4 Dividing Radicals 601 6.5 Adding and Subtracting Radical

Expressions 611 6.6 Solving Radical Equations 621

CHAPTER 6

CHAPTER 6


Quadratic Equations 635


7.1

7.2

Solving Quadratic Equations: Special Cases 637 The Pythagorean Theorem 649

7.3 Solving Quadratic Equations: Completing the Square 659

7.4 Solving Quadratic Equations: The Quadratic Formula 673

7.5 Quadratic Equations: A Review 685



Linear Equations with Two Variables 699


8.1 Equations with Two Variables 703 8.2 Rectangular Coordinate System 713 8.3 Graphs of Linear Equations 725 8.4 Slope and Intercepts 741 8.5 Graphing Linear Equations Using Slope and

Intercept 755 8.6 Graphs of Linear Inequalities 769

CHAPTER 8

CHAPTER 8


Systems of Equations 787


9.1 Systems of Equations: Solving by Graphing 791

9.2 Systems of Equations: Solving by Substitution 807

9.3 Systems of Equations: Solving by Addition 827



Appendix I Appendix II

Appendix III Appendix IV

Appendix V Appendix VI

Appendix VII

The Properties of Zero A.l Prime Factors of Numbers 1 Through 100 A.3 Formulas A.4 Metrie Measures and Equivalents A.7 Graph Paper A.8 Squares and Square Roots (0 to 199) A.10 Calculators A . l l

Midterm Examination A.15 Final Examination A.17 Answers to Exercises A.19 Index 1.1

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