### Maximal Ideals, Cosets, Polynomials and Quotient Rings

Consider the ring of Z[x] and its ideal (2, ) Find the size of Z[x] / (2, ) and find a coset representative for each coset of Z[x] / (2, ) ; Is the Z[x] / (2, ) a field (You need to prove it) ? Is the Z[x] / (2, ) an integral domain (You need to prove it)