ALGEBRA FOR COLLEGE STUDENTS

ALGEBRA FOR COLLEGE STUDENTS

Jerome E. Kaufmann
Karen L. Schwitters
Seminole Sure College a! Plasma

CONTENTS

1 Basic Concepts and Properties 1
1.1 Sets, Real Numbers, and Numerical Expressions 2
1.2 Operations with Real Numbers 10
1.3 Properties of Real Numbers and the Use of Exponents 20
1.4 Algebraic Expressions 27
Chapter 1 Summary 36
Chapter 1 Review Problem Set 38
Chapter 1 Test 40

2 Equations, Inequalities, and Problem Solving 41
2.1 Solving First-Degree Equations 42
2.2 Equations Involving Fractional Forms 49
2.3 Equations Involving Decimals and Problem Solving 57
2.4 Formulas 64
2.5 Inequalities 74
2.6 More on Inequalities and Problem Solving 81
2.7 Equations and Inequalities Involving Absolute Value 90
Chapter 2 Summary 97
Chapter 2 Review Problem Set 101
Chapter 2 Test 104
Chapters 1– 2 Cumulative Review Problem Set 105

3 Polynomials 107
3.1 Polynomials: Sums and Differences 108
3.2 Products and Quotients of Monomials 114
3.3 Multiplying Polynomials 119
3.4 Factoring: Greatest Common Factor and Common Binomial Factor 127
3.5 Factoring: Difference of Two Squares and Sum or Difference of Two Cubes 135
3.6 Factoring Trinomials 141
3.7 Equations and Problem Solving 149
Chapter 3 Summary 155
Chapter 3 Review Problem Set 158
Chapter 3 Test 161

4 Rational Expressions 163
4.1 Simplifying Rational Expressions 164
4.2 Multiplying and Dividing Rational Expressions 169
4.3 Adding and Subtracting Rational Expressions 175
4.4 More on Rational Expressions and Complex Fractions 182
4.5 Dividing Polynomials 190
4.6 Fractional Equations 196
4.7 More Fractional Equations and Applications 202
Chapter 4 Summary 211
Chapter 4 Review Problem Set 216
Chapter 4 Test 218
Chapters 1– 4 Cumulative Review Problem Set 219

5 Exponents and Radicals 221
5.1 Using Integers as Exponents 222
5.2 Roots and Radicals 229
5.3 Combining Radicals and Simplifying Radicals That Contain Variables 238
5.4 Products and Quotients Involving Radicals 243
5.5 Equations Involving Radicals 249
5.6 Merging Exponents and Roots 254
5.7 Scientific Notation 259
Chapter 5 Summary 265
Chapter 5 Review Problem Set 269
Chapter 5 Test 271

6 Quadratic Equations and Inequalities 273
6.1 Complex Numbers 274
6.2 Quadratic Equations 281
6.3 Completing the Square 289
6.4 Quadratic Formula 293
6.5 More Quadratic Equations and Applications 300
6.6 Quadratic and Other Nonlinear Inequalities 308
Chapter 6 Summary 314
Chapter 6 Review Problem Set 318
Chapter 6 Test 320
Chapters 1– 6 Cumulative Review Problem Set 321

7 Linear Equations and Inequalities in Two Variables 323
7.1 Rectangular Coordinate System and Linear Equations 324
7.2 Linear Inequalities in Two Variables 337
7.3 Distance and Slope 342
7.4 Determining the Equation of a Line 353
7.5 Graphing Nonlinear Equations 363
Chapter 7 Summary 371
Chapter 7 Review Problem Set 376
Chapter 7 Test 379

8 Functions 381
8.1 Concept of a Function 382
8.2 Linear Functions and Applications 391
8.3 Quadratic Functions 398
8.4 More Quadratic Functions and Applications 407
8.5 Transformations of Some Basic Curves 416
8.6 Combining Functions 425
8.7 Direct and Inverse Variation 432
Chapter 8 Summary 440
Chapter 8 Review Problem Set 447
Chapter 8 Test 449
Chapters 1– 8 Cumulative Review Problem Set 450

9 Polynomial and Rational Functions 453
9.1 Synthetic Division 454
9.2 Remainder and Factor Theorems 458
9.3 Polynomial Equations 463
9.4 Graphing Polynomial Functions 473
9.5 Graphing Rational Functions 483
9.6 More on Graphing Rational Functions 492
Chapter 9 Summary 499
Chapter 9 Review Problem Set 503
Chapter 9 Test 504

10 Exponential and Logarithmic Functions 505
10.1 Exponents and Exponential Functions 506
10.2 Applications of Exponential Functions 513
10.3 Inverse Functions 524
10.4 Logarithms 534
10.5 Logarithmic Functions 542
10.6 Exponential Equations, Logarithmic Equations, and Problem Solving 549
Chapter 10 Summary 559
Chapter 10 Review Problem Set 565
Chapter 10 Test 567
Chapters 1– 10 Cumulative Review Problem Set 568

11 Systems of Equations 571
11.1 Systems of Two Linear Equations in Two Variables 572
11.2 Systems of Three Linear Equations in Three Variables 582
11.3 Matrix Approach to Solving Linear Systems 589
11.4 Determinants 598
11.5 Cramer’s Rule 607
11.6 Partial Fractions (Optional) 613
Chapter 11 Summary 619
Chapter 11 Review Problem Set 623
Chapter 11 Test 625

12 Algebra of Matrices 627
12.1 Algebra of 2x2 Matrices 628
12.2 Multiplicative Inverses 634
12.3 mxn Matrices 640
12.4 Systems of Linear Inequalities: Linear Programming 649
Chapter 12 Summary 658
Chapter 12 Review Problem Set 662
Chapter 12 Test 664
Chapters 1 – 12 Cumulative Review Problem Set 665

13 Conic Sections 669
13.1 Circles 670
13.2 Parabolas 676
13.3 Ellipses 684
13.4 Hyperbolas 693
13.5 Systems Involving Nonlinear Equations 702
Chapter 13 Summary 709
Chapter 13 Review Problem Set 714
Chapter 13 Test 715

14 Sequences and Mathematical Induction 717
14.1 Arithmetic Sequences 718
14.2 Geometric Sequences 725
14.3 Another Look at Problem Solving 733
14.4 Mathematical Induction 738
Chapter 14 Summary 744
Chapter 14 Review Problem Set 746
Chapter 14 Test 748

Appendix A Prime Numbers and Operations with Fractions 749
Appendix B Binomial Theorem 757
Answers to Odd-Numbered Problems and All Chapter Review, Chapter Test, Cumulative Review and Appendix A Problems 761