Prove that a homoegenous polynomial on $K^{n+1}$ of degree $ d<|K|$, vanishes at $|K|$ points oth the line $\mathbb{P}^1 \subset \mathbb{P}^n$ then vanishes on $\mathbb{P}^1$.
Very much struggling with this problem I believe it is meant to be analogous to polynomial to the proof a non zero Polynomial on $K^{n}$ of degree $ d<|K|$, vanishes at more than $d$ points on the line $L$, $a +tv$ then it vanishes on the line.
Really would appreciate the help or some hints.