# How do you find the quotient of (n^2+3n+10)div(n-1) using long division?

May 25, 2018

$n - 4$ and remainder of$\frac{6}{n - 1}$

#### Explanation:

$\textcolor{w h i t e}{\ldots \ldots \ldots .} \textcolor{w h i t e}{\ldots \ldots \ldots \ldots} n - 4$
$n - 1 | \overline{{n}^{2} + 3 n + 10}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots} \underline{{n}^{2} - n}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots .} 4 n + 10$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots .} \underline{4 n + 04}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} 6$

$\frac{{n}^{2} + 3 n + 10}{n - 1} = n - 4 + \frac{6}{n - 1}$