# How do you divide ( x^3-4x^2-17x+60 )/(3-2x)?

Feb 3, 2018

$- \frac{1}{2} {x}^{2} + \frac{5}{4} x + \frac{83}{8} + \frac{231}{8 \left(3 - 2 x\right)} \text{ Corrected}$

#### Explanation:

$\textcolor{w h i t e}{\text{-----------------------------}} + {x}^{3} - 4 {x}^{2} - 17 x + 60$
$\textcolor{m a \ge n t a}{- \frac{1}{2} {x}^{2}} \left(3 - 2 x\right) \to \textcolor{w h i t e}{\text{-----")ul(+x^3-3/2x^2 larr" Subtract }}$
color(white)("--------------------------------")0color(white)("-")-5/2x^2-17x+60 color(red)(larr" Corrected"
$\textcolor{m a \ge n t a}{+ \frac{5}{4} x} \left(3 - 2 x\right) \to \textcolor{w h i t e}{\text{------------") ul(-5/2x^2+15/4x larr" Subtract}}$
$\textcolor{w h i t e}{\text{---------------------------------------")0 color(white)("----}} - \frac{83}{4} x + 60$

$\textcolor{m a \ge n t a}{+ \frac{83}{8}} \left(3 - 2 x\right) \to \textcolor{w h i t e}{\text{----------------------")ul(-83/4x+249/8larr" Subt.}}$
color(magenta)("Remainder"->color(white)("--------------------------------") 0+231/8)

Giving:

$\textcolor{m a \ge n t a}{- \frac{1}{2} {x}^{2} + \frac{5}{4} x + \frac{83}{8} + \frac{231}{8 \left(3 - 2 x\right)}}$

Feb 3, 2018

$- \frac{1}{2} {x}^{2} + \frac{5}{4} x + \frac{83}{8} + \frac{231}{8 \left(- 2 x + 3\right)}$

#### Explanation:

$\frac{{x}^{3} - 4 {x}^{2} - 17 x + 60}{3 - 2 x}$

$\textcolor{w h i t e}{\ldots \ldots \ldots .} \textcolor{w h i t e}{\ldots} - \frac{1}{2} {x}^{2} + \frac{5}{4} x + \frac{83}{8}$
$- 2 x + 3 | \overline{{x}^{3} - 4 {x}^{2} - 17 x + 60}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} \underline{{x}^{3} - \frac{3}{2} {x}^{2}}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots .} - \frac{5}{2} {x}^{2} - 17 x$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots .} \underline{- \frac{5}{2} {x}^{2} + \frac{15}{4} x}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots} - \frac{83}{4} x + 60$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} \underline{- \frac{83}{4} x + \frac{249}{8}}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots} \frac{231}{8}$

$\frac{{x}^{3} - 4 {x}^{2} - 17 x + 60}{3 - 2 x} = - \frac{1}{2} {x}^{2} + \frac{5}{4} x + \frac{83}{8} + \frac{231}{8 \left(- 2 x + 3\right)}$