Let $R = \mathbb{F}_2[X]$. Choose the correct statement(s) from below:\\
(A) $R$ has uncountably many maximal ideals;\\
(B) Every maximal ideal of $R$ has infinitely many elements;\\
(C) For all maximal ideals $\mathfrak{m}$ of $R$, $R/\mathfrak{m}$ is a finite field;\\
(D) For every integer $n$, every ideal of $R$ has only finitely many elements of degree $\leq n$.