Factoring 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"