@Bootmaker let F be a field, then F[x] is a polynomial ring, and F(c) would be the ring (extension field?) constructed from F[x] by substituting x with c. Since F(c) is also a ring we could construct a polynomial ring from it, i.e. F(c)[x].

That question was asking to find a polynomial in Q(pi^3)[x] where pi^2+1 is a root.

Now I realize maybe I should have called it "polynomial ring on extension field", but from that name it's not obvious that two levels of polynomials are involved.

@w3cing: My prof told me to always find simple examples in matrices, polynomials, number theory and physics to simplify the thought process.

To simplify it, …all those math words just mean polynomials in two variables…? 🤯