# How do you divide (x^3-8x^2-6) / (x-2)?

Jun 24, 2018

The quotient is $= {x}^{2} - 6 x - 12$ and the remainder is $- 30$

#### Explanation:

Perform a long division

$\textcolor{w h i t e}{a a a a}$${x}^{3} - 8 {x}^{2} + 0 x - 6$$\textcolor{w h i t e}{a a a a}$$|$$x - 2$

$\textcolor{w h i t e}{a a a a}$${x}^{3} - 2 {x}^{2}$$\textcolor{w h i t e}{a a a a a a a a a a a a}$$|$${x}^{2} - 6 x - 12$

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

$\textcolor{w h i t e}{a a a a a a}$$- 6 {x}^{2} + 12 x$

$\textcolor{w h i t e}{a a a a a a a a a}$$0 - 12 x - 6$

$\textcolor{w h i t e}{a a a a a a a a a a a}$$- 12 x + 24$

$\textcolor{w h i t e}{a a a a a a a a a a a a a a a}$$0 - 30$

The quotient is $= {x}^{2} - 6 x - 12$ and the remainder is $- 30$

$\frac{{x}^{3} - 8 {x}^{2} - 6}{x - 2} = {x}^{2} - 6 x - 12 - \frac{30}{x - 2}$