# How do you divide (x^3 - 2x^2 - 3)/(x^2-x+1)?

Jul 15, 2018

The remainder is $= \left(- 2 x - 2\right)$ and the quotient is $= \left(x - 1\right)$

#### Explanation:

Perform a long division

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

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

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

$\textcolor{w h i t e}{a a a a a a a}$$- 1 {x}^{2} + 1 x - 1$

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

The remainder is $= \left(- 2 x - 2\right)$ and the quotient is $= \left(x - 1\right)$

$\frac{{x}^{3} - 2 {x}^{2} + 0 x - 3}{{x}^{2} - x + 1} = \left(x - 1\right) - \frac{2 x + 2}{{x}^{2} - x + 1}$