In this problem I have a trinomial where my leading coefficient is not 1, that's a 3 right there which means it's going to be a difficult factoring problem I’m going to have to grab a pencil and get ready to do some guess and checking.
Here's what I know, I know that the product of my first terms needs to be 3 and the product of my last terms need to be -8. And I’m kind of happy because there’s only two things that multiply to 3, 3 and 1, so I’m going to start with 3x and x. I know that my answer is going to start like that.
From there I’m going to be guessing and checking using numbers that multiply to -8. I'm just going to guess 8 and 1, I’m going to choose one to be negative I don't know -8 and 1, I’m just guessing here and I’m going to plug them in guessing where they go checking using FOIL.
So let me try Foiling I have 3x² take away 24x to add x take away 8. Shoot that's not right because when I combine my middle terms I don't get that answer. So that's not the correct answer I’m going to start it again.
3x and x these are kind of bummer you guys, these are not easy problems. Again I want to look for two numbers that multiply to -8 and by the way you'll get better at this with more practice, you'll be able to do more steps in your head that will help you kind of Foil in your brain as you go.
So I’m going to try now using 2 and 4. I just picked that I’m going to try -2, +4 one of them has to be negative because the product is negative but they can't both be negative. Okay I disguise let's check by Foiling 3x² that's my first, outers oh-oh, I think I did it right take away 8. Yes I know I did it right because when I combine these middle terms I do get -2. So I’m a happy camper.
Foiling told me that I had done this problem correctly. That's just how you go through it guys. You use what you know, we knew the first two numbers had to multiply with 3; so it had to be 3 in 1 and then here I was just guessing pairs that multiplied to -8 and I guessed where I’d put them.
First I guessed one and -8, I was wrong so then I guessed again 4 and 2. It might have been that if I tried -4 there and 2 it wouldn't work I had to get +4 match up with the 3x and -2 matched up with the x. There's only one right answer for you guys and I’m telling you now it’s a drag especially when you start trying this for the first time but I promise they get easier as you do more and more. Don't give up you can do them.
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M.A. in Secondary Mathematics, Stanford University B.S., Stanford University
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