# How do you divide (-x^3 - x^2-6x+5 )/((-x + 10 )?

Feb 21, 2016

(−x^3−x^2−6x+5)/(-x+10) is

${x}^{2} + 11 x + 116 - \frac{1155}{- x + 10}$

#### Explanation:

To divide −x^3−x^2−6x+5 by $- x + 10$, first we observe that $- x$ goes $\frac{- {x}^{3}}{-} x = {x}^{2}$ times in $- {x}^{3}$.

Hence, x^2(-x+10)-10x^2−x^2−6x+5 or
(note we have added and subtracted 10x^2) x^2(-x+10)-11x^2−6x+5

As $- 11 {x}^{2} / - x = 11 x$, above can be written is

x^2(-x+10)+11x(-x+10)-110x−6x+5 or

${x}^{2} \left(- x + 10\right) + 11 x \left(- x + 10\right) - 116 x + 5$

and as $- 116 \frac{x}{-} x = 116$, above can be written as

${x}^{2} \left(- x + 10\right) + 11 x \left(- x + 10\right) + 116 x \left(- x + 10\right) - 1160 + 5$ or

${x}^{2} \left(- x + 10\right) + 11 x \left(- x + 10\right) + 116 x \left(- x + 10\right) - 1155$ or

$\left({x}^{2} + 11 x + 116\right) \left(- x + 10\right) - 1155$ or

Hence (−x^3−x^2−6x+5)/(-x+10)# is

${x}^{2} + 11 x + 116 - \frac{1155}{- x + 10}$