In the detailed proof, when trying to show Q(x) is a non-zero polynomial, the argument arrives at the situation where P(R(x)) = 0 as a rational function in F(x), where R(x) = f(x)/g(x). Given that P(y) is a non-zero polynomial, what is the direct reason this situation implies that R(x) is a constant:
A) If R(x) where a non-constant rational function, then P(R(x)) would necessarily be a non-zero rational function, directly contradicting P(R(x)) = 0.
B) If R(x) were a non-zero rational function, it would mean that `alpha` is a root of P(y), which is a contradiction to `alpha` being transcendental ?