# How do you divide (5m^3 - 7m^2 + 14) / (m^2 - 2)?

Here , quotient" =>(5m- 7) $\text{and Remainder} = 10 m$
$\frac{5 {m}^{3} - 7 {m}^{2} + 14}{{m}^{2} - 2}$
$\implies \frac{\left(5 m \left({m}^{2} - 2\right) + 10 m - 7 \left({m}^{2} - 2\right) - \cancel{14} + \cancel{14}\right)}{{m}^{2} - 2}$
$\implies \frac{\left(5 m \left({m}^{2} - 2\right) - 7 \left({m}^{2} - 2\right) + 10 m\right)}{{m}^{2} - 2}$
$\implies \left(\frac{5 m \left({m}^{2} - 2\right)}{{m}^{2} - 2} - 7 \frac{{m}^{2} - 2}{{m}^{2} - 2} + \frac{10 m}{{m}^{2} - 2}\right)$
$\implies \left(5 m - 7 + \frac{10 m}{{m}^{2} - 2}\right)$