Factoring

Date: 9/5/95 at 0:1:30
From: Anonymous
Subject: algebra

Question:
How do I solve x^2+x-12=0 ?

Date: 9/6/95 at 12:11:50
From: Doctor Ken
Subject: Re: algebra

Hello!

The way that most people like to solve problems like this is to FACTOR the 
expression x^2 + x - 12.  I'll do an example that's similar to yours, then 
see whether you can do your problem.  I'll do x^2 + x - 30 = 0.

First figure out all the ways you can factor
30 as the product of two numbers: 

1 x 30
2 x 15
3 x 10
5 x 6

Then, since we're going to have something in the form of
(x - one factor)(x + the other factor), we use this to decide which of the
pairs of factors we should use.  At this point, it's kind of guess-and-check.

The key here is that we're looking for factors that have a difference of 1.
That's because the coefficent on the x term is 1.  So looking down the list, 
it looks like 5 x 6 will work.  Should we use (x - 5)(x + 6), or 
(x - 6)(x + 5)?  Well, the first one gives us x^2 + x - 30, and the second
gives us x^2 - x - 30.  So we use the first one.

Once we have that, we know that x is either 5 or -6.

Do you see how you might do you your problem now?  Factoring is 
something that really takes a lot of practice to get good at.

- Doctor Ken,  The Geometry Forum