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# Intermediate Algebra : Concepts and Applications

**by**Bittinger, Marvin L.; Ellenbogen, David J.

6th

### 9780201708486

0201708485

Hardcover

1/1/2002

Addison Wesley

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## Summary

The Sixth Edition of Intermediate Algebra: Concepts and Applications continues to bring your students a best-selling text that incorporates the five-step problem-solving process, real-world applications, proven pedagogy, and an accessible writing style. The Bittinger/Ellenbogen hardback series has consistently provided teachers and students with the tools needed to succeed in developmental mathematics. With this revision, the authors have maintained all the hallmark features that have made this series so successful, including its five-step problem-solving process, student-oriented writing style, real-data applications, and wide variety of exercises. Among the features added or revised are new Aha! exercises that encourage students to think before jumping in to solve a problem, 20% new and added real-data applications, and 50% more new Skill Maintenance Exercises. This series not only provides students with the tools necessary to learn and understand math, but also provides them with insights into how math works in the world around them.

## Table of Contents

Preface | p. xi |

Algebra and Problem Solving | |

Some Basics of Algebra | p. 2 |

Operations and Properties of Real Numbers | p. 11 |

Solving Equations | p. 22 |

Connecting the Concepts | p. 25 |

Introduction to Problem Solving | p. 29 |

Formulas, Models, and Geometry | p. 39 |

Properties of Exponents | p. 46 |

Scientific Notation | p. 56 |

Summary and Review | p. 64 |

Test | p. 68 |

Graphs, Functions, and Linear Equations | |

Graphs | p. 70 |

Functions | p. 78 |

Linear Functions: Slope, Graphs, and Models | p. 93 |

Another Look at Linear Graphs | p. 106 |

Other Equations of Lines | p. 117 |

Connecting the Concepts | p. 122 |

The Algebra of Functions | p. 126 |

Summary and Review | p. 135 |

Test | p. 138 |

Systems of Linear Equations and Problem Solving | |

Systems of Equations in Two Variables | p. 142 |

Solving by Substitution or Elimination | p. 151 |

Connecting the Concepts | p. 156 |

Solving Applications: Systems of Two Equations | p. 159 |

Systems of Equations in Three Variables | p. 172 |

Connecting the Concepts | p. 172 |

Solving Applications: Systems of Three Equations | p. 181 |

Elimination Using Matrices | p. 186 |

Determinants and Cramer's Rule | p. 191 |

Business and Economic Applications | p. 197 |

Summary and Review | p. 203 |

Test | p. 206 |

Cumulative Review: Chapters 1-3 | p. 207 |

Inequalities and Problem Solving | |

Inequalities and Applications | p. 212 |

Intersections, Unions, and Compound Inequalities | p. 224 |

Absolute-Value Equations and Inequalities | p. 233 |

Inequalities in Two Variables | p. 242 |

Connecting the Concepts | p. 249 |

Applications Using Linear Programming | p. 252 |

Summary and Review | p. 260 |

Test | p. 263 |

Polynomials and Polynomial Functions | |

Introduction to Polynomials and Polynomial Functions | p. 266 |

Connecting the Concepts | p. 266 |

Multiplication of Polynomials | p. 277 |

Common Factors and Factoring by Grouping | p. 287 |

Connecting the Concepts | p. 287 |

Factoring Trinomials | p. 293 |

Factoring Perfect-Square Trinomials and Differences of Squares | p. 303 |

Factoring Sums or Differences of Cubes | p. 309 |

Factoring: A General Strategy | p. 313 |

Applications of Polynomial Equations | p. 317 |

Summary and Review | p. 329 |

Test | p. 332 |

Rational Expressions, Equations, and Functions | |

Rational Expressions and Functions: Multiplying and Dividing | p. 334 |

Rational Expressions and Functions: Adding and Subtracting | p. 343 |

Complex Rational Expressions | p. 352 |

Rational Equations | p. 361 |

Connecting the Concepts | p. 361 |

Solving Applications Using Rational Equations | p. 368 |

Division of Polynomials | p. 378 |

Synthetic Division | p. 383 |

Formulas, Applications, and Variation | p. 388 |

Summary and Review | p. 401 |

Test | p. 404 |

Cumulative Review: Chapters 1-6 | p. 405 |

Exponents and Radicals | |

Radical Expressions and Functions | p. 408 |

Rational Numbers as Exponents | p. 416 |

Multiplying Radical Expressions | p. 423 |

Dividing Radical Expressions | p. 429 |

Expressions Containing Several Radical Terms | p. 435 |

Solving Radical Equations | p. 443 |

Connecting the Concepts | p. 443 |

Geometric Applications | p. 450 |

The Complex Numbers | p. 458 |

Summary and Review | p. 466 |

Test | p. 469 |

Quadratic Functions and Equations | |

Quadratic Equations | p. 472 |

The Quadratic Formula | p. 483 |

Applications Involving Quadratic Equations | p. 490 |

Studying Solutions of Quadratic Equations | p. 498 |

Equations Reducible to Quadratic | p. 502 |

Quadratic Functions and Their Graphs | p. 508 |

Connecting the Concepts | p. 514 |

More About Graphing Quadratic Functions | p. 517 |

Problem Solving and Quadratic Functions | p. 523 |

Polynomial and Rational Inequalities | p. 532 |

Summary and Review | p. 540 |

Test | p. 544 |

Exponential and Logarithmic Functions | |

Composite and Inverse Functions | p. 548 |

Exponential Functions | p. 560 |

Connecting the Concepts | p. 560 |

Logarithmic Functions | p. 569 |

Properties of Logarithmic Functions | p. 576 |

Common and Natural Logarithms | p. 583 |

Solving Exponential and Logarithmic Equations | p. 590 |

Applications of Exponential and Logarithmic Functions | p. 596 |

Summary and Review | p. 610 |

Test | p. 613 |

Cumulative Review: Chapters 1-9 | p. 615 |

Conic Sections | |

Conic Sections: Parabolas and Circles | p. 620 |

Conic Sections: Ellipses | p. 631 |

Conic Sections: Hyperbolas | p. 639 |

Connecting the Concepts | p. 643 |

Nonlinear Systems of Equations | p. 649 |

Summary and Review | p. 658 |

Test | p. 660 |

Sequences, Series, and the Binomial Theorem | |

Sequences and Series | p. 662 |

Arithmetic Sequences and Series | p. 668 |

Geometric Sequences and Series | p. 677 |

The Binomial Theorem | p. 688 |

Connecting the Concepts | p. 688 |

Summary and Review | p. 696 |

Test | p. 698 |

Cumulative Review: Chapters 1-11 | p. 699 |

The Graphing Calculator | p. 703 |

Answers | p. 1 |

Index | p. 1 |

Index of Applications | |

Videotape and CD Index | |

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