I'm not sure what exactly your approach would be. Originally, I just posted my approach:

If 2 is a zero of the polynomial, then (x - 2) is a factor.

(By polynomial long-division)

Therefore, the other zero is -1

But having re-read your first post, I think that might be what you would have done anyway. I'm not sure that I know any more efficient method. But I suggest you just divide once and then factorise, that - at least - might make things a little faster?