Polynomials/Maximal degree/Finite dimensional linear subspace/Exercise

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

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