How to Factor Polynomials

Date: 14 Mar 1995 16:42:05 -0500
From: Sandip Mody
Subject: Factoring Polynomials

Hi, I am having trouble factoring the following polynomials:
6a^2y^2+5ay^2-6y^2 and 3ax^2+7ax+2a.

I would appreciate if you could show me step by step instructions and 
possibly even more examples.  Thank you.

Date: 19 Mar 1995 01:28:39 -0500
From: Dr. Sydney
Subject: Re: Factoring Polynomials

Hello!

Sorry we didn't get back to you sooner.  When factoring polynomials, look
for numbers or variables that are common to all parts of the polynomial.
For instance, in your first example, look first at the variables.  Are there
a's in each part of the polynomial?  The first two terms both have an a, but
the last term doesn't.  Are there y's in each part of the polynomial?  Yes,
in fact there is a y^2 in each part of the polynomial.  So, you can first
factor out a y^2.  Then you get :  Y^2(6a^2 + 5a - 6).  Now the problem
is to factor 6a^2 + 5a - 6 .  This is just a standard quadratic you are
probably more used to factoring.  Can you figure out what it factors into?

Go through the same process with the second problem. Can you factor out an
a?  How about an x?  Any constants?

The best way to learn how to factor polynomials is to practice a lot.  So,
keep working, and I'm sure you will get it.  If you have any other
questions, feel free to write back!

--Sydney, "Dr. Math"