# How do you find the quotient of (9m^3-6m^2+3m+2)div(m-1) using long division?

Jul 21, 2018

$9 {m}^{2} + 3 m + \frac{2}{m - 1}$

#### Explanation:

$\left(9 {m}^{3} - 6 {m}^{2} + 3 m + 2\right) \div \left(m - 1\right)$

$\textcolor{w h i t e}{\ldots \ldots \ldots .} \textcolor{w h i t e}{\ldots \ldots \ldots \ldots} 9 {m}^{2} + 3 m$
$m - 1 | \overline{9 {m}^{3} - 6 {m}^{2} + 3 m + 2}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} \underline{9 {m}^{3} - 9 {m}^{2}}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} 3 {m}^{2} - 3 m$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} \underline{3 {m}^{2} - 3 m}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots} 0 + 0 + 2$

$\frac{9 {m}^{3} - 6 {m}^{2} + 3 m + 2}{m - 1} = 9 {m}^{2} + 3 m + \frac{2}{m - 1}$