SOLUTION: I am trying to learn, with great difficulty, how to factor this type of problem... 2a^2-2ab-24b^2 ... I have tried factoring out the 2, but I don't know how to go any further with

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Question 7131: I am trying to learn, with great difficulty, how to factor this type of problem... 2a^2-2ab-24b^2 ... I have tried factoring out the 2, but I don't know how to go any further with this problem. How do I find the factors of 12 if there is no factor for the prceding term? Thank you so much for your help.
Found 2 solutions by Earlsdon, glabow:
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Well, you could start by factoring a 2 from the expression, just to simplify it a bit.
=
Now let's look at the expression in the parentheses:
The factors of the first term , would be
Look at the last term: and ask what are the factors of this term?
= or just to name a couple.
So, now try: Using the FOIL method, multiply these factors:
Simplify to get:
and if you multiply by the 2 we factored at the start, we'll get:

So, the factors are:

Answer by glabow(165) (Show Source):
You can put this solution on YOUR website!
This is one of those things that have two approaches. One is art and the other is science. In this case, the art way is easier.
The polynomial
has an obvious factor, 2.
must be factored into binomials where
the term comes from a times a
the term comes from mb times nb, where m times n = -12
the term comes from a times mb plus a time nb, where m plus n = -1
The numbers -4 and 3 satisfy the requirements: -4 times 3 = -12, and -4 plus 3 = -1.
So the factors are
The orginal polynomial is