- Decide which of the following are ideals of the ring Z[z] (and justify your answer): (a) the set of all polynomials whose constant term is a multiple of 3 (b) the set of all polynomials whose coefficient of r² is a multiple of 3 (c) the set of all polynomials whose constant term, coefficient of , and coefficient of 2²are zero (d) Z[²] (i.e., the polynomials in which only even powers of a appear) (e) the set of polynomials whose coefficients sum to zero (f) the set of polynomials p(x) such that p'(0) = 0, where p'(x) is the usual first derivative of p(x) with respect to r.