# How do you divide (-2x^3+7x^2-4x-1)/(3x-1) ?

Aug 9, 2018

$- \frac{2}{3} {x}^{2} + \frac{19}{9} x - \frac{17}{27} - \frac{44}{81 x - 27}$

#### Explanation:

$\textcolor{w h i t e}{\text{ddddddd.ddddddd}} - 2 {x}^{3} + 7 {x}^{2} - 4 x - 1$
$\textcolor{m a \ge n t a}{- \frac{2}{3} {x}^{2}} \left(3 x - 1\right) \to \underline{- 2 {x}^{3} + \frac{2}{3} {x}^{2} \leftarrow \text{ Subtract}}$
$\textcolor{w h i t e}{\text{ddddddddddddddddd}} 0 + \frac{19}{3} {x}^{2} - 4 x - 1$

color(magenta)(+19/9x)(3x-1)->color(white)("ddddd.")ul(19/3x^2-19/9xlarr" Subtract")
$\textcolor{w h i t e}{\text{dddddddddddddddddddddd")0color(white)("dd}} - \frac{17}{9} x - 1$

$\textcolor{m a \ge n t a}{- \frac{17}{27}} \left(3 x - 1\right) \to \textcolor{w h i t e}{\text{dddddddddddd")ul( -17/9x+17/27larr" Subtract}}$
color(magenta)("Remainder"-> color(white)("ddddddddddddddddd")0color(white)("d")-44/27)

$\textcolor{m a \ge n t a}{- \frac{2}{3} {x}^{2} + \frac{19}{9} x - \frac{17}{27} - \left[\frac{44}{27} \textcolor{b l a c k}{\div \left(3 x - 1\right)}\right]}$

$- \frac{2}{3} {x}^{2} + \frac{19}{9} x - \frac{17}{27} - \frac{44}{81 x - 27}$