For (i), recognize J as the set of polynomials with even constant term. Any principal generator has to divide everything in J, which in particular contains all the constant polynomials {2, 4, 6, ...}. The only possibilities are 1 and 2. Since J is not the whole ring, 1 is not a generator. And 2 doesn't generate all of J, since it generates polynomials withalleven coefficients.

For (ii), a hint: describe I similarly to how we described J above. If pq is in I, then what do you know about the constant terms of p and q?