# Polynomials/Maximal degree/Finitedimensional linear subspace/Exercise

Let ${\displaystyle {}K}$ be a field and let ${\displaystyle {}K[X]}$ denote the polynomial ring over ${\displaystyle {}K}$. Let ${\displaystyle {}d\in \mathbb {N} }$. Show that the set of all polynomials of degree ${\displaystyle {}\leq d}$ is a finite dimensional subspace of ${\displaystyle {}K[X]}$. What is its