Inactive Tutor answered • 04/09/13
If this is supposed to say x2 + 3x -10 = 0, we can factor this polynomial to help us find the answer. Factoring the polynomial gives us (x + 5)(x - 2) = 0. Now, we know that anything multiplied by zero gives us zero, so it can either be the case that (x + 5) = 0, or (x - 2) = 0. This is the case if x = -5 or x = 2. So we have two possible answers.
Is your question is about how to perform the factorization, i.e. the process of turning x2 + 3x - 10 into (x + 5)(x - 2) ? To see how to do this, we need to realize that what we're looking for is a pair of factors of -10 that add up to 3. We can start by listing the factors of -10 in pairs: (-1,10), (1,-10), (2,-5), and (-2,5). If I add the numbers in each of these pairs I get -1 + 10 = 9, 1 - 10 = -9, 2 - 5 = -3, and -2 + 5 = 3. So the last pair gives us what we want. From that I can write (x + 5)(x - 2), and if I use FOIL, we can double check that this gives us the original polynomial.
