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Question

Based on this part of the proof,what does it mean that `alpha` is algebraic over `F(beta)`:
A) `alpha` does not fit any polynomial, and `F(alpha , beta)` is just F(beta) with `alpha` added freely.
B) `alpha` fits a polynomial with coefficients in `F(beta)`, and `F(alpha , beta)` grows a fixed amount over `F(beta)` ?