Suppose $T \in \mathcal L(V,W)$ and $U$ is a subspace of $V$. Let $\pi$ denote the quotient map from $V$ onto $V/U$. Prove that there exists $S \in \mathcal L(V/U,W)$ such that $T = S \circ \pi$ if and only if $U \subset \text{null }T$.

TODO