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Review of the Methods of Factoring - Problem 3

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Factoring a trinomial without any common factors; so behind me I have a fairly, I would say ugly trinomial just because we have fairly big numbers that we’re dealing with 16, 24 and 9. They could be bigger, but they’re fairly big in this scheme of things and so what we want to do is factor this down.

And the first thing I look for in this case is to see if we’re dealing with perfect squares. I mean by that is 16x² is a perfect square and as is 9y². So the easiest thing for us to think about is, is this going to be a quantity squared? In order to get a 16x², you have to have 4x, and in order to get the 9y² we would need a 3y.

Your last term is positive which means that signs need to agree. Our middle term is negative which means we have to have a negative inside, and so this takes care of our outer two terms, but we need to double check to make sure this middle term is actually what we get when we FOIL this out.

Our FOIL out we’d end up with a -12 if we multiply this together, but we have our inner and our outers, so we have our two middle terms, we have these two and these two both of which are going to give us -12, two -12s is -24, so what we actually have here is a binomial squared.

The cool thing about factoring is that it’s always pretty easy to check to make sure you’re factored answer works and always FOIL it out and if you get the same thing you did it right. If you get something different something went wrong.

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