Complete the proofs of Theorem 17.1 and Corollary 17.1.
Let R[x] be a polynomial ring.
a) If R is commutative, then R [x] is commutative.
b) If R is a ring with unity, then R[x] is a ring with unity.
c) R[x] is an integral domain if and only if R is an integral domain.
If R is a ring, then under the operations of addition and multiplication given in Eqs (1) and
(2), (R[x], +, ∙) is a ring, called the polynomial ring, or ring of polynomials, over R.