Problems: Let Z[x] denote the ring of polynomials in x with integer coefficients. This is an integral domain. (You do not need to check that.) (a) Show that I = {f(x) = Z[x] | ƒ (¦¹) = 0} is a prime ideal in Z[x]. (b) Let I be as above. Show that it is not a maximal ideal in Z[x].