Let I = <x^2 + 5x +6> = {(x^2 + 5x+6) *f| f in Q[x]} Does the factor ring Q[x]/I have any zero divisors?
Clearly, x^2 +5x+6 is not irreducible as it equals (x+2)(x+3), thus Q[x]/I is not a field, however I am having difficulty showing whether or not it is an integral domain.