Solution
= Solution
{c}
The <monomials> $1,x,\ldots,x^n$ form a <basis> of $V_n$: they <span> every <polynomial> of <degree of a polynomial> at most $n$, and equality of <polynomials> forces equality of every coefficient, proving <linear independence>. Therefore
$$
\boxed{\dim_{\mathbb C}V_n=n+1.}
$$
The <zero polynomial> is included in $V_n$ even though its <degree of a polynomial> need not be assigned an ordinary nonnegative value.