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 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.