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
Real Exponents This is a short acknowledgment that the
exponent properties from the previous two sections will hold for any real exponent.
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.
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
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.