Factoring Rules

Date: 6/28/96 at 14:58:57
From: Anonymous
Subject: Factoring Rules

Dear Dr. Math.

   I asked you a factoring question and your explanation and procedure 
to finding the answer was so clear that I've been wondering if there 
is a clear set of factoring rules or procedures that would help me 
with these difficult factoring exercises. I'll be going into 9th grade 
next September. 

Thank you. 
           Jackie

Date: 6/28/96 at 17:44:11
From: Doctor Gary
Subject: Re: Factoring Rules

  Factoring will always be more art than skill (although there are 
algorithms which will permit you to factor quadratic or cubic 
expressions, the former being much easier than the latter).

 The best way to improve your skill at factoring is to do some 
multiplying.  For example, when you multiply (x+2) by (x-3), you'll 
notice that the product has a term of x^2, a term of -6 and a third, 
composite, term of (2-3)x.

  More generally, whenever, you multiply (x+m) by (x+n), the product 
will have a term of x^2, a term of mn and a composite term of (m+n)x.

  When the time comes that you have to factor something like:

   x^2 -3x -10,

you'll know to be thinking in terms of some "m" and "n" such that mn 
is equal to -10 and (m+n) is equal to -3.

  Good luck, and happy factoring.

-Doctor Gary,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/