Further, since , at least two of the sets  and C are non-empty and by computing the above GCDs we may obtain non-trivial factors. Since the ring of polynomials over a field is a Euclidean domain, we may compute these GCDs using the Euclidean algorithm.
Additionally, since at least two of sets A and C are non-empty, and by calculating their greatest common divisors (GCD), we can find non-trivial factors.  Since the ring of polynomials over a field is a Euclidean domain, we can use the Euclidean algorithm to compute these GCDs.