# How do you divide (-x^4-4x^3-3x^2+4x-2)/(x^2+4) ?

##### 1 Answer
Dec 13, 2017

color(magenta)(-x^2-4x+1 plus remainder of color(magenta)(20x-6

#### Explanation:

$\frac{- {x}^{4} - 4 {x}^{3} - 3 {x}^{2} + 4 x - 2}{{x}^{2} + 4}$

color(white)(..........)color(white)(.)color(magenta)(-x^2-4x+1
$w - 2 | \overline{- 4 {x}^{4} - 4 {x}^{3} - 3 {x}^{2} + 4 x - 2}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots . .} \underline{- {x}^{4} + 0 x - 4 {x}^{2}}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots} - 4 {x}^{3} + {x}^{2} + 4 x$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots .} \underline{- 4 {x}^{3} + 0 x - 16 x - 2}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} {x}^{2} + 20 x - 2$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} \underline{{x}^{2} + 0 x + 4}$
color(white)(..........................................)color(magenta)(20x-6

(-x^4-4x^3-3x^2+4x-2)/(x^2+4) = color(magenta)(-x^2-4x+1 plus remainder of color(magenta)(20x-6