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Algebra (Notes) / Preliminaries   [Notes] [Practice Problems] [Assignment Problems]

Algebra - Notes
  Next Chapter Solving Equations and Inequalities
  Next Section Integer Exponents

 Preliminaries

The purpose of this chapter is to review several topics that will arise time and again throughout this material.  Many of the topics here are so important to an Algebra class that if you don’t have a good working grasp of them you will find it very difficult to successfully complete the course.  Also, it is assumed that you’ve seen the topics in this chapter somewhere prior to this class and so this chapter should be mostly a review for you.  However, since most of these topics are so important to an Algebra class we will make sure that you do understand them by doing a quick review of them here.

 

Exponents and polynomials are integral parts of any Algebra class.  If you do not remember the basic exponent rules and how to work with polynomials you will find it very difficult, if not impossible, to pass an Algebra class.   This is especially true with factoring polynomials.  There are more than a few sections in an Algebra course where the ability to factor is absolutely essential to being able to do the work in those sections.  In fact, in many of these sections factoring will be the first step taken.

 

It is important that you leave this chapter with a good understanding of this material!  If you don’t understand this material you will find it difficult to get through the remaining chapters.  Here is a brief listing of the material covered in this chapter.

 

Integer Exponents  In this section we will start looking at exponents and their properties.

Rational Exponents  We will define rational exponents in this section and extend the properties from the previous section to rational exponents.

Radicals  Here we will define radical notation and relate radicals to rational exponents.  We will also give the properties of radicals.

Polynomials  We will introduce the basics of polynomials in this section including adding, subtracting and multiplying polynomials.

Factoring Polynomials  This is the most important section of all the preliminaries.  Factoring polynomials will appear in pretty much every chapter in this course.  Without the ability to factor polynomials you will be unable to complete this course.

Rational Expressions  In this section we will define rational expressions and discuss adding, subtracting, multiplying and dividing them.

Complex Numbers  Here is a very quick primer on complex numbers and how to manipulate them.

  Next Section Integer Exponents
  Next Chapter Solving Equations and Inequalities

Algebra (Notes) / Preliminaries    [Notes] [Practice Problems] [Assignment Problems]

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