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Factoring Trinomials, a = 1 - Problem 2
Here I’m given a trinomial with the leading coefficient as one. But I have something that’s’ a little tricky here I have a minus sign so when I’m asked to factor this, this tells me the product of two numbers gives me the answer -10. If you have 2 numbers and the answer is negative that means one of your numbers has to be a negative value. I’m going to keep that in mind while I’m looking for things that multiply to -10 and add up to +3. So numbers that multiply to 10 might be a pair of 1 and 10 or 2 and 5 and that’s it, those are the only pairs. So it’s going to be some combination of these with some pluses and minuses. One has to be negative; one has to be positive so that when I add them up the answer is positive three. A lot of you guys can do that pretty quickly.
Notice that if I were to use +5 and -2 the product would be -10 and the sum would be +3. So there’s my factors, p minus 2 and p plus 5. That’s the factored form of this trinomial. Check your work by foiling just to make sure firsts, outers, inners, lasts combine this and you’ll see that we did do it correctly. We have 3p as the middle term there and we know we did it right.
So what I want to leave you with is if you see a negative signs before your c term that means one of your numbers that go into the factors is going to be negative the other one’s going to be positive. So you want to keep that in mind when you’re looking for your factor pairs for the c term.