# How do you divide (x^2 + 7x – 6) / (x-6)  using polynomial long division?

Aug 5, 2018

$\left({x}^{2} + 7 x - 6\right) = \left(x - 6\right) \left(x + 13\right) + 72$

#### Explanation:

Here ,

Dividend $: \textcolor{b l u e}{{x}^{2} + 7 x - 6} \mathmr{and}$ divisor : color(red)(x-6

So ,
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} \underline{x + 13 \textcolor{w h i t e}{\ldots \ldots \ldots}} \leftarrow q u o t i e n t$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots} \left(x - 6\right)$ $|$ ${x}^{2} + 7 x - 6$
color(white)(......)color(violet)((x-6)*xtocolor(white)(......)ul(x^2-6x)$\textcolor{w h i t e}{\ldots \ldots .} \Leftarrow \text{subtract}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .0} 13 x - 6$
color(white)(..........)color(violet)((x-6)*13tocolor(white)(.......)ul(13x-78)$\textcolor{w h i t e}{\ldots \ldots .} \Leftarrow \text{subtract}$
color(white)(....................................................)color(green)(72$\textcolor{w h i t e}{\ldots \ldots \ldots} \leftarrow \text{Remainder}$
Hence ,

$\left({x}^{2} + 7 x - 6\right) = \left(x - 6\right) \left(x + 13\right) + 72$

$Q u o t i e n t : q \left(x\right) = x + 13$ $\text{and Remainder } : r \left(x\right) = 72$