Alg_FindingZeroesOfPolynomials

# Alg_FindingZeroesOfPolynomials - Preface Here are my online...

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Preface Here are my online notes for my Algebra course that I teach here at Lamar University, although I have to admit that it’s been years since I last taught this course. At this point in my career I mostly teach Calculus and Differential Equations. Despite the fact that these are my “class notes” they should be accessible to anyone wanting to learn Algebra or needing a refresher in for algebra. I’ve tried to make the notes as self contained as possible and do not reference any book. However, they do assume that you’ve has some exposure to the basics of algebra at some point prior to this. While there is some review of exponents, factoring and graphing it is assumed that not a lot of review will be needed to remind you how these topics work. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed. 1. Because I wanted to make this a fairly complete set of notes for anyone wanting to learn algebra I have included some material that I do not usually have time to cover in class and because this changes from semester to semester it is not noted here. You will need to find one of your fellow class mates to see if there is something in these notes that wasn’t covered in class. 2. Because I want these notes to provide some more examples for you to read through, I don’t always work the same problems in class as those given in the notes. Likewise, even if I do work some of the problems in here I may work fewer problems in class than are presented here. 3. Sometimes questions in class will lead down paths that are not covered here. I try to anticipate as many of the questions as possible in writing these up, but the reality is that I can’t anticipate all the questions. Sometimes a very good question gets asked in class that leads to insights that I’ve not included here. You should always talk to someone who was in class on the day you missed and compare these notes to their notes and see what the differences are. 4. This is somewhat related to the previous three items, but is important enough to merit its own item. THESE NOTES ARE NOT A SUBSTITUTE FOR ATTENDING CLASS!! Using these notes as a substitute for class is liable to get you in trouble. As already noted not everything in these notes is covered in class and often material or insights not in these notes is covered in class.

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Finding Zeroes of Polynomials We’ve been talking about zeroes of polynomial and why we need them for a couple of sections now. We haven’t, however, really talked about how to actually find them for polynomials of degree greater than two. That is the topic of this section. Well, that’s kind of the topic of this section. In general, finding all the zeroes of any polynomial is a fairly difficult process. In this section we will give a process that will find all rational ( i.e. integer or fractional) zeroes of a polynomial. We will be able to use the process for finding all the zeroes of a polynomial provided all but at most two of the zeroes are rational.

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## This note was uploaded on 11/12/2011 for the course MATH 101 taught by Professor Fisher during the Fall '11 term at Rutgers.

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Alg_FindingZeroesOfPolynomials - Preface Here are my online...

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