Q: Factor 5c²-18c-8
A: Okay, factoring will look something like this:
5c²-18c-8 = (ac – b)(dc + e)
Where a, b, d and e are all just numbers. Remember, c is our variable!
I know that a*d = 5 and that b*e = 8.
a & d can either be 1 & 5 or 5 & 1 (the only factors of 5).
b & e can be 1 & 8 (or flipped) or 2 & 4 (or flipped)…. Hmmmm.. Let’s try:
5c²-18c-8… The problem is the middle term, -18c. We have to make sure to chose correctly so the middle term comes out as -18.
5c²-18c-8 = (5c – 2)(c + 4)??? Does that work? Check to see if 5c*4 – 2*c equals -18c?? But, 5c*4 – 2*c = +18c. That just means that I need to switch the signs… Like so:
5c²-18c-8 = (5c + 2)(c – 4)! Tada, this works.
Remember, factoring (as I do it) involves guessing and checking. Good thing I chose to use 2 & 4… If I had chose to use 1 & 8 as my numbers, I would have hit a dead end and had to do even more guess/check work. The more you practice, the better you get at guessing and checking, creating less work for yourself. There are other factoring methods to avoid guessing and checking, which I will discuss in a later post.