Consider $3u^{2}v^{3}+5uv^{2}-2u^{3}v^{4}$. Factor out $uv^{2}$.
$$uv^{2}\left(3uv+5-2u^{2}v^{2}\right)$$
Consider $3uv+5-2u^{2}v^{2}$. Consider $3uv+5-2u^{2}v^{2}$ as a polynomial over variable $u$.
$$-2v^{2}u^{2}+3vu+5$$
Find one factor of the form $kv^{m}u^{n}+p$, where $kv^{m}u^{n}$ divides the monomial with the highest power $-2v^{2}u^{2}$ and $p$ divides the constant factor $5$. One such factor is $2uv-5$. Factor the polynomial by dividing it by this factor.
