Let R be a commutative ring with identity and let be a polynomial in

Prove that is a zero divisor of if and only if there is a nonzero element such that

Proof so far.

Suppose that is a zero divisor, then by definition such that

But how would I factor this down into one single element?

Conversely, suppose that , then would I be able to find a polynomial that behaves like s?

Thank you!