# How do you factor 10m^3n^2-15m^2n+25m?

$10 {m}^{3} {n}^{2} - 15 {m}^{2} n + 25 m = 5 m \left(2 {m}^{2} {n}^{2} - 3 m n + 5\right)$
To see that this does not factor further, let $p = m n$.
Then $2 {m}^{2} {n}^{2} - 3 m n + 5 = 2 {p}^{2} - 3 p + 5$
If this had linear factors, then it would factorise as $\left(2 p - 1\right) \left(p - 5\right)$ or $\left(2 p - 5\right) \left(p - 1\right)$ in order to get the coefficient of ${p}^{2}$ and the constant term correct. Neither of these works.