In the Polynomial Interpolation Theorem, you have r(x) = p(x) - r(x), but I think it should be q(x) = p(x) - r(x).

Fixed, thank you! (it's actually r(x)=p(x)-q(x))

(proof-reading through HN is a mildly embarrassing process, sorry about that! I do go over these posts and proof-read them several times myself before publishing)