# How do you divide (x^3-7x-6) / (x+1)?

Jul 1, 2018

The quotient is $= {x}^{2} - x - 6$ and the remainder is $= 0$

#### Explanation:

Perform a long division

$\textcolor{w h i t e}{a a a a}$${x}^{3} + 0 {x}^{2} - 7 x - 6$$\textcolor{w h i t e}{a a a a}$$|$$x + 1$

$\textcolor{w h i t e}{a a a a}$${x}^{3} + {x}^{2}$$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$|$${x}^{2} - x - 6$

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

$\textcolor{w h i t e}{a a a a a a a}$$- {x}^{2} - x$

$\textcolor{w h i t e}{a a a a a a a}$$- 0 - 6 x - 6$

$\textcolor{w h i t e}{a a a a a a a a a a a}$$- 6 x - 6$

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

The quotient is $= {x}^{2} - x - 6$ and the remainder is $= 0$

$\frac{{x}^{3} + 0 {x}^{2} - 7 x - 6}{x + 1} = {x}^{2} - x - 6$

Jul 1, 2018

${x}^{2} - x - 6$

#### Explanation:

Given: $\frac{{x}^{3} - 7 x - 6}{x + 1}$

Using place keepers of no value. Example: $0 {x}^{2}$

$\textcolor{w h i t e}{\text{ddddd.ddddd.d}} {x}^{3} + 0 {x}^{2} - 7 x - 6$
$\textcolor{red}{+ {x}^{2}} \left(x + 1\right) \to \underline{{x}^{3} + {x}^{2} \leftarrow \text{ Subtract}}$
$\textcolor{w h i t e}{\text{dddddddddddd.}} 0 - {x}^{2} - 7 x - 6$
$\textcolor{red}{- x} \left(x + 1\right) \to \textcolor{w h i t e}{\text{dd.")ul(-x^2-x larr" Subtract}}$
$\textcolor{w h i t e}{\text{dddddddddddddddd}} 0 - 6 x - 6$
$\textcolor{red}{- 6} \left(x + 1\right) \to \textcolor{w h i t e}{\text{dddddd.")ul(-6x-6larr" Subtract}}$
color(white)("dddddddddddddddddddd")0+0 larr" Remainder"

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$\frac{{x}^{3} - 7 x - 6}{x + 1} = \textcolor{red}{{x}^{2} - x - 6}$