Q:  Factor this:  -3x² + 12x – 12

A:  Before I start factoring, I look to see if there is any number that I can “pull out” (this is techinically called the “greatest common factor method”).  See how each number is divisible by 3?  So, I can pull a 3 out…. But, I even like to pull the – out too, so I will pull out a -3 like so:

-3x² + 12x – 12 = -3 (x² – 4x + 3)

So, now we have this:  -3 (x² – 4x + 3)

Now, we ask ourselves:  What two numbers multiply to give +3 and combine to get -4.  The answer is -1 and -3… -1*-3 = 3 and -1 + -3 = -4.

So, we can factor like so:

-3 (x² – 4x + 3) = -3(x – 1)(x – 3)

You can FOIL that back out to make sure it worked!