Hi Sarah,

Let f(x) = 2x³ + 3x² - 32x + 15. I looked and didn't see any obvious factorization so the next technique to try is to guess at a number a so that f(a) = 0. After a few attempts I found that f(3) = 0 and thus that factor theorem says that

f(x) = (x - 3) g(x)

for some polynomial g(x). Hence g(x) = f(x)/(x - 3). You can then find g(x) either by long division or by synthetic division. g(x) is a quadratic which hopefully you will be able to factor.

I hope this helps,
Penny