# How do you divide ( -x^3+ 4x^2+8x-7 )/(x - 2 )?

May 2, 2017

$- {x}^{2} + 2 x + 12 + \frac{17}{x - 2}$

#### Explanation:

One way is to use the divisor as a factor in the numerator.

$\textcolor{m a \ge n t a}{\text{Add / Subtract "" terms incurred as a result}}$

$\text{Consider the numerator}$

$\textcolor{red}{- {x}^{2}} \left(x - 2\right) \textcolor{m a \ge n t a}{- 2 {x}^{2}} + 4 {x}^{2} + 8 x - 7$

$= \textcolor{red}{- {x}^{2}} \left(x - 2\right) \textcolor{red}{+ 2 x} \left(x - 2\right) \textcolor{m a \ge n t a}{+ 4 x} + 8 x - 7$

$= \textcolor{red}{- {x}^{2}} \left(x - 2\right) \textcolor{red}{+ 2 x} \left(x - 2\right) \textcolor{red}{+ 12} \left(x - 2\right) \textcolor{m a \ge n t a}{+ 24} - 7$

$= \textcolor{red}{- {x}^{2}} \left(x - 2\right) \textcolor{red}{+ 2 x} \left(x - 2\right) \textcolor{red}{+ 12} \left(x - 2\right) + 17$

$\text{quotient "=color(red)(-x^2+2x+12)" remainder } = 17$

$\Rightarrow \frac{- {x}^{3} + 4 {x}^{2} + 8 x - 7}{x - 2} = - {x}^{2} + 2 x + 12 + \frac{17}{x - 2}$