# How do you factor 18m² n^4-12m² n^3+24m² n²?

$18 {m}^{2} {n}^{4} - 12 {m}^{2} {n}^{3} + 24 {m}^{2} {n}^{2}$
$= 6 {m}^{2} {n}^{2} \left(3 {n}^{2} - 2 n + 4\right)$
$\left(3 {n}^{2} - 2 n + 4\right)$ has no simpler linear factors since it's discriminant is negative:
$\Delta \left(3 {n}^{2} - 2 n + 4\right) = {\left(- 2\right)}^{2} - \left(4 \times 3 \times 4\right)$
$= 4 - 48 = - 44$