# What is (6x^3-18x^2-12x)/(-6x)?

##### 2 Answers
Jun 3, 2018

$- {x}^{2} + 3 x + 2$

#### Explanation:

$\text{each term on the numerator is divided by } - 6 x$

$= \frac{6 {x}^{3}}{- 6 x} - \frac{18 {x}^{2}}{- 6 x} - \frac{12 x}{- 6 x}$

$= \frac{\cancel{6} {x}^{\left(3 - 1\right)}}{-} \cancel{6} - \frac{{\cancel{18}}^{3} {x}^{\left(2 - 1\right)}}{- {\cancel{6}}^{1}} - {\cancel{12 x}}^{2} / \left(- {\cancel{6 x}}^{1}\right)$

$= - {x}^{2} + 3 x + 2$

Jun 3, 2018

color(crimson)(-x^2+3x+2

#### Explanation:

color(crimson)((6x^3-18x^2-12x)/(-6x)

$\textcolor{w h i t e}{. .} \textcolor{w h i t e}{\ldots .} - {x}^{2} + 3 x + 2$
$- 6 x | \overline{6 {x}^{3} - 18 {x}^{2} - 12 x}$
$\textcolor{w h i t e}{\ldots \ldots \ldots .} 6 {x}^{3}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} \overline{- 18 {x}^{3}}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} \underline{- 18 {x}^{3}}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} - 12 x$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} \underline{- 12 x}$

color(crimson)((6x^3-18x^2-12x) / (-6x) = -x^2+3x+2