Work

6

Factoring Polynomials

and Solving Equations

6.1 Introduction to

Factoring

6.2 Factoring Trinomials I

(x 2

bx

c)

6.3 Factoring Trinomials II

(ax2

bx

c)

6.4 Special Types of

Factoring

6.5 Summary of Factoring

6.6 Solving Equations by

Factoring I (Quadratics)

6.7 Solving Equations by

Factoring II (Higher

Degree)

What we see depends

mainly on what we look

for.

—JOHN LUBBOCK

M

ost cars are designed so that their exteriors are curved and smooth. This characteristic is especially true for solar cars. In fact, a side view of a solar car often resembles the cross section of an airplane wing, as illustrated in the accompanying figure. This

design reduces drag from air resistance and increases fuel efficiency.

Views of a Solar Car and a Standard Car

ISBN 1-256-49082-2

Mathematics plays an important role in the design of cars. Third-degree polynomials

called cubic splines are used extensively by engineers to obtain a smooth shape for new

cars. Although the topic of cubic splines is covered in advanced mathematics and engineering courses, in this chapter we introduce many concepts necessary for understanding

polynomials and polynomial equations.

Source: R. Burden and J. Faires.

Numerical Analysis.

359

Beginning and Intermediate Algebra with Applications & Visualization, Third edition, by Gary K. Rockswold and Terry A. Krieger. Published by Addison Wesley.

Copyright © 2013 by Pearson Education, Inc.

360

CHAPTER 6 F ACTORING POLYNOMIALS AND SOLVING EQUATIONS

6.1

Introduction to Factoring

Basic Concepts ● Common Factors ● Factoring by Grouping

A LOOK INTO MATH N

Polynomials are frequently used in applications to approximate data and to model such

things as changes in the weather, sales of a new video game, and the growth of young children. As a result, scientists and mathematicians commonly solve equations involving polynomials. One way to solve these equations is to use factoring. In this section we introduce

two basic methods of factoring polynomials.

Basic...