Reason being, because of the Polynomial Remainder Theorem, the remainder of a polynomial when divided by is such that . Proof of why this happens in the link. It's not definetely NOT complicated, but it's senseless to just glue it here.
As for your problem, it's a pretty much direct application. You want the remainder of that division to be -10, so . This leaves you with an equation with one unknown. Now just solve for k.