Not homework, test review - help with determining valid subspaces 10) Determine which of the following sets is a subspace of Pn for an
    appropriate value of n.

EXPLAIN/PROVE WHY OTHERS ARE NOT VECTOR SPACES.

$B$ isn't closed under vector addition, and it doesn't include the zero vector. It only includes polynomials with degree exactly $4$. Let $f=x^4+1$ and let $g=-x^4$. Both are in $B$, but their sum is not, because it has degree $0$.
You're right about $C$. The restriction there also makes $C$ not closed under multiplication by the scalar $-1$.
