Question

What 2 numbers multiply to -147 but add to -14?

Answer 1

Okay, so let's go over multiplying negative numbers.  A positive times a positive is a positive, right?  But a negative times a negative is also a positive.  Only a negative times a positive (or a positive times a negative) gives you a negative number.  So, we know that one of our 2 numbers in this question must be negative; the other must be positive.

Let's now take a look at the factors of -147, starting with the positives.  Obviously, -147 and 1 are factors: -147 * 1 = -147.  What other factors of -147 are there?

What about 7?  Try it: -147 / 7 = -21.  So here are two factors: -21, and 7.  They multiply to -147.  Do they add up to -14?  Let's see: -21+7 = 7+(-21) = 7-21= -14.  Yup, that works!

Answer: -21 and 7