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

May 4, 2017

The quotient is $= 5 m - 7$ and the remainder is $= 10 m$

#### Explanation:

We perform a long division

$\textcolor{w h i t e}{a a a a}$$5 {m}^{3} - 7 {m}^{2}$$\textcolor{w h i t e}{a a a a a a}$$+ 14$$|$${m}^{2} - 2$

$\textcolor{w h i t e}{a a a a}$$5 {m}^{3}$$\textcolor{w h i t e}{a a a a}$$- 10 m$$\textcolor{w h i t e}{a a a a a a}$|5m-7

$\textcolor{w h i t e}{a a a a}$$0 - 7 {m}^{2}$$\textcolor{w h i t e}{a a a a a a a a a}$$+ 14$

$\textcolor{w h i t e}{a a a a a a}$$- 7 {m}^{2}$$\textcolor{w h i t e}{a a a a a a a a a}$$+ 14$

$\textcolor{w h i t e}{a a a a a a a a}$$- 0 + 10 m$$\textcolor{w h i t e}{a a a a}$$+ 0$

Therefore,

$\left(5 {m}^{3} - 7 {m}^{2} + 14\right) = \left({m}^{2} - 2\right) \left(5 m - 7\right) + 10 m$