D. FR ANKLIN WRIGHT ALGEBRA for COLLEGE STUDENTS © All Rights Reser ved.Editor: Nina Waldron Vice President of Development: Marcel Prevuznak Production Editor: Kara Roché Associate Editor: Barry Wright, III Editorial Assistant: Liz Allen Copy Editors: Jessica Ballance, Bethany Bates, Phillip Bushkar, Kimberly Cumbie, Taylor Hamrick, Susan Niese, Sundar Parthasarathy, Claudia Vance, Colin Williams Answer Key Editors: Ashley Godbold, Bill Epperson, Kirk Boyer, Michael Lane Contributor: Elizabeth Thomas Layout: E. Jeevan Kumar, D. Kanthi, U. Nagesh, B. Syamprasad Art: Ayvin Samonte Cover Layout: Jennifer Moran A division of Quant Systems, Inc. 546 Long Point Rd., Mount Pleasant, SC 29464 © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written consent of the publisher. Printed in the United States of America Library of Congress Control Number: 2015942651 ISBN: Student Textbook: 978-1-941552-15-5 Student Textbook and Software Bundle: 978-1-941552-13-1 © All Rights Reser ved.TABLE OF CONTENTS 1.1 Prime Numbers, Exponents, and LCM 2 1.2 Introduction to Real Numbers 8 1.3 Operations with Real Numbers 25 1.4 Linear Equations in One Variable: ax + b = c 39 1.5 Evaluating and Solving Formulas 51 1.6 Applications 58 1.7 Solving Inequalities in One Variable 72 Chapter 1 Index of Key Ideas and Terms 88 Chapter 1 Chapter Review 96 Chapter 1 Chapter Test 100 Chapter 1 Real Numbers and Solving Equations 1 Preface ix Hawkes Learning Systems: Algebra for College Students xxi 2.1 Cartesian Coordinate System and Linear Equations: Ax + By = C 104 2.2 Slope-Intercept Form: y = mx + b 118 2.3 Point-Slope Form: y - y1 = m(x - x1) 134 2.4 Introduction to Functions and Function Notation 144 2.5 Graphing Linear Inequalities: y < mx + b 165 Chapter 2 Index of Key Ideas and Terms 173 Chapter 2 Chapter Review 177 Chapter 2 Chapter Test 184 Chapters 1-2 Cumulative Review 186 Chapter 2 Linear Equations and Functions 103 3.1 Systems of Linear Equations in Two Variables 192 3.2 Applications 204 3.3 Systems of Linear Equations in Three Variables 212 3.4 Matrices and Gaussian Elimination 224 3.5 Determinants 239 3.6 Cramer’s Rule 249 3.7 Graphing Systems of Linear Inequalities 256 Chapter 3 Index of Key Ideas and Terms 263 Chapter 3 Chapter Review 269 Chapter 3 Chapter Test 274 Chapters 1-3 Cumulative Review 276 Chapter 3 Systems of Linear Equations 191 TABLE OF CONTENTS © All Rights Reser ved.TABLE OF CONTENTS 4.1 Exponents and Scientific Notation 280 4.2 Addition and Subtraction with Polynomials 296 4.3 Multiplication with Polynomials 305 4.4 Division with Polynomials 315 4.5 Introduction to Factoring Polynomials 323 4.6 Factoring Trinomials 329 4.7 Special Factoring Techniques 340 4.8 Polynomial Equations and Applications 348 4.9 Using a Graphing Calculator to Solve Equations 361 Chapter 4 Index of Key Ideas and Terms 368 Chapter 4 Chapter Review 374 Chapter 4 Chapter Test 379 Chapters 1-4 Cumulative Review 381 Chapter 4 Exponents and Polynomials 279 5.1 Multiplication and Division with Rational Expressions 386 5.2 Addition and Subtraction with Rational Expressions 397 5.3 Complex Fractions 408 5.4 Solving Equations with Rational Expressions 413 5.5 Applications 425 5.6 Variation 436 Chapter 5 Index of Key Ideas and Terms 448 Chapter 5 Chapter Review 452 Chapter 5 Chapter Test 456 Chapters 1-5 Cumulative Review 458 Chapter 5 Rational Expressions and Rational Equations 385 6.1 Roots and Radicals 462 6.2 Rational Exponents 477 6.3 Operations with Radicals 489 6.4 Equations with Radicals 500 6.5 Functions with Radicals 506 6.6 Introduction to Complex Numbers 517 6.7 Multiplication and Division with Complex Numbers 524 Chapter 6 Index of Key Ideas and Terms 531 Chapter 6 Chapter Review 537 Chapter 6 Chapter Test 541 Chapters 1-6 Cumulative Review 543 Chapter 6 Roots, Radicals, and Complex Numbers 461 © All Rights Reser ved.TABLE OF CONTENTS 7.1 Solving Quadratic Equations 548 7.2 The Quadratic Formula: x bbac a = −±−2 4 2 561 7.3 Applications 570 7.4 Equations in Quadratic Form 580 7.5 Graphing Quadratic Functions: Parabolas 587 7.6 Solving Quadratic and Rational Inequalities 605 Chapter 7 Index of Key Ideas and Terms 622 Chapter 7 Chapter Review 627 Chapter 7 Chapter Test 631 Chapters 1-7 Cumulative Review 633 Chapter 7 Quadratic Equations and Quadratic Functions 547 8.1 Algebra of Functions 638 8.2 Composition of Functions and Inverse Functions 652 8.3 Exponential Functions 669 8.4 Logarithmic Functions 683 8.5 Properties of Logarithms 690 8.6 Common Logarithms and Natural Logarithms 700 8.7 Logarithmic and Exponential Equations and Change-of-Base 709 8.8 Applications 718 Chapter 8 Index of Key Ideas and Terms 725 Chapter 8 Chapter Review 730 Chapter 8 Chapter Test 737 Chapters 1-8 Cumulative Review 740 Chapter 8 Exponential and Logarithmic Functions 637 9.1 Translations 746 9.2 Parabolas as Conic Sections 761 9.3 Distance Formula and Circles 770 9.4 Ellipses and Hyperbolas 782 9.5 Nonlinear Systems of Equations 796 Chapter 9 Index of Key Ideas and Terms 803 Chapter 9 Chapter Review 808 Chapter 9 Chapter Test 811 Chapters 1-9 Cumulative Review 813 Chapter 9 Conic Sections 745 © All Rights Reser ved.TABLE OF CONTENTS 10.1 Sequences 818 10.2 Sigma Notation 826 10.3 Arithmetic Sequences 832 10.4 Geometric Sequences and Series 843 10.5 The Binomial Theorem 856 Chapter 10 Index of Key Ideas and Terms 865 Chapter 10 Chapter Review 869 Chapter 10 Chapter Test 873 Chapters 1-10 Cumulative Review 875 Chapter 10 Sequences, Series, and the Binomial Theorem 817 A.1 Review of Fractions 879 A.2 Synthetic Division and the Remainder Theorem 888 A.3 Pi 894 A.4 Powers, Roots, and Prime Factorizations 896 Appendix Answers 899 Index 959 © All Rights Reser ved.vii PREFACE PREFACE Purpose and Style Algebra for College Students provides a solid base for further studies in mathematics. In particular, business and social science majors who will continue their studies in statistics and calculus will be well prepared for success in those courses. With feedback from users, insightful comments from reviewers, and skillful editing and design by the editorial staff at Hawkes Learning Systems, we have confidence that students and instructors alike will find that this text is indeed a superior teaching and learning tool. The text may be used independently or in conjunction with the software package Hawkes Learning Systems: Algebra for College Students developed by Quant Systems. We have provided very little overlap with material covered in a beginning algebra course. While Chapter 1 provides a review of topics from beginning algebra, students will find that the review is comprehensive and that the pace of coverage is somewhat faster and in more depth than they have seen in previous courses. As with any text in mathematics, students should read the text carefully and thoroughly. The style of the text is informal and nontechnical while maintaining mathematical accuracy. Each topic is developed in a straightforward step-by-step manner. Each section contains many carefully developed and worked out examples to lead the students successfully through the exercises and prepare them for examinations. Whenever appropriate, information is presented in list form for organized learning and easy reference. Common errors are highlighted and explained so that students can avoid such pitfalls and better understand the correct corresponding techniques. Practice problems with answers are provided in nearly every section to allow the students to “warm up” and to provide the instructor with immediate classroom feedback. A special feature in many sections is "Writing and Thinking About Mathematics." The related questions are placed at the end of the Exercises for the section and ask the students to delve deeper into mathematical concepts and to become accustomed to organizing their thoughts and writing about mathematics in their own words. The NCTM and AMATYC curriculum standards have been taken into consideration in the development of the topics throughout the text. In particular: • there is an emphasis on reading and writing skills as they relate to mathematics, • techniques for using a graphing calculator are discussed early, • a special effort has been made to make the exercises motivating and interesting, • geometric concepts are integrated throughout, and • statistical concepts, such as interpreting bar graphs and calculating elementary statistics, are included where appropriate. © All Rights Reser ved.viii PREFACE Presented before the first section of every chapter, this feature prefaces the subject of the chapter and its purpose. Introduction A feature at the beginning of every chapter that presents some interesting math history related to the chapter at hand. Did You Know? The objectives provide the students with a clear and concise list of skills presented in each section. Objectives © All Rights Reser ved.ix PREFACE Examples are denoted with titled headers indicating the problem solving skill being presented. Each section contains many carefully ex- plained examples with appropriate tables, diagrams, and graphs. Ex- amples are presented in an easy to understand, step-by-step fashion and annotated with notes for addi- tional clarification. Examples Notes highlight common mistakes and give addi- tional clarification to more subtle details. Notes Definitions are presented in highly visible boxes for easy reference. Definition Boxes © All Rights Reser ved.Next >