# How do you divide ( x^4-2x^3-8x+16 )/(4x-6)?

##### 1 Answer
Nov 30, 2017

$\frac{1}{4} {x}^{3} - \frac{1}{8} {x}^{2} - \frac{3}{16} x - 2 \frac{9}{32}$and remainder of $29 \frac{11}{16}$

#### Explanation:

$\frac{{x}^{4} - 2 {x}^{3} - 8 x + 16}{4 x - 6}$

$\textcolor{w h i t e}{\ldots \ldots \ldots .} \textcolor{w h i t e}{.} \frac{1}{4} {x}^{3} - \frac{1}{8} {x}^{2} - \frac{3}{16} x - 2 \frac{9}{32}$
$4 x - 6 | \overline{{x}^{4} - 2 {x}^{3} + 0 x - 8 x + 16}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} \underline{{x}^{4} - \frac{3}{2} {x}^{3}}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} - \frac{1}{2} {x}^{3} + 0 x$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots} \underline{- \frac{1}{2} {x}^{3} + \frac{3}{4} {x}^{2}}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots} - \frac{3}{4} {x}^{2} - 8 x$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} \underline{- \frac{3}{4} {x}^{2} + \frac{9}{8} x}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots} - \frac{73}{8} x + 16$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} \underline{- \frac{73}{8} x - \frac{438}{32}}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} \frac{950}{32} = 29 \frac{11}{16}$

$\frac{{x}^{4} - 2 {x}^{3} - 8 x + 16}{4 x - 6} = \frac{1}{4} {x}^{3} - \frac{1}{8} {x}^{2} - \frac{3}{16} x - 2 \frac{9}{32}$and remainder of$29 \frac{11}{16}$