Factoring Trinomials, a = 1 - Problem 3

This problem I have a trinomial where my b value is negative but c is positive. Keep in mind this is the product of my two values, this is their sum. I’m looking for two numbers that multiply to a positive answer but add up to a negative answer. That means I’m looking for two negative values. A negative times a negative is a positive and when I add them up I also have a negative answer, so now I need to think of what 2 numbers multiply to 10, add up to -7 and there both going to be negative numbers.

Well things that multiply to 10 are either 1 or 10. That’s not going to work because they don’t ever add up to anything close to 7. Or 5 and 2: in our case -5 and -2, because is need them to add up to a negative number and multiply to a positive number. There they are. That’s my factored form.

I’m going to go through and FOIL just to check; firsts, outers, inners, lasts. And I can already see in my brain when I combine those middle terms I will have -7. That’s how I know it's right. I just wanted to show you guys one of the tricks of how to approach these problems. It gets a lot trickier when you don’t have a 1, if you have like a 2 or something there. So it’s important that you spend time now looking for patterns when you have positives and negatives showing up in your coefficients.