One of the final steps in learning to factor trinomials is factoring trinomials with "a" not equal to one. In this case, "a" is the leading coefficient, or the coefficient of the squared term. When factoring trinomials with "a" not equal to one, in addition to using the methods used when "a" is one we must take the factors of "a" into account when finding the terms of the factored binomials.
Here I'm given a trinomial with a leading coefficient is 1 but I have something that's 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 two 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 when I'm looking for things that multiplied a negative 10 and add up to positive 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 positive so that when I add them up the answer is positive 3. A lot of you guys can do that pretty quickly notice that if I were to use positive 5 and -2 the products will be -10 and the sum will be +3, so there's my factors p take away 2 and p+5 that's the factored form of this trinomial. Check you work by foiling just to make sure first, outers, inners, last combine these 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 sign before you c term that means one of your numbers that go into your factor is going to be negative the other one is going to be positive, so you want to keep that in mind when you're looking at your factor pairs for the c term.