# How do you divide (6x^3-12x+10) div (3x-3)?

Jun 18, 2017

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

#### Explanation:

$\text{one way is to use the divisor as a factor in the numerator}$

$\text{consider the numerator}$

$\textcolor{red}{2 {x}^{2}} \left(3 x - 3\right) \textcolor{m a \ge n t a}{+ 6 {x}^{2}} - 12 x + 10$

$= \textcolor{red}{2 {x}^{2}} \left(3 x - 3\right) \textcolor{red}{+ 2 x} \left(3 x - 3\right) \textcolor{m a \ge n t a}{+ 6 x} - 12 x + 10$

$= \textcolor{red}{2 {x}^{2}} \left(3 x - 3\right) \textcolor{red}{+ 2 x} \left(3 x - 3\right) \textcolor{red}{- 2} \left(3 x - 3\right) \textcolor{m a \ge n t a}{- 6} + 10$

$= \textcolor{red}{2 {x}^{2}} \left(3 x - 3\right) \textcolor{red}{+ 2 x} \left(3 x - 3\right) \textcolor{red}{- 2} \left(3 x - 3\right) + 4$

$\Rightarrow \frac{6 {x}^{3} - 12 x + 10}{3 x - 3}$

$= \frac{\cancel{\left(3 x - 3\right)} \left(\textcolor{red}{2 {x}^{2} + 2 x - 2}\right)}{\cancel{\left(3 x - 3\right)}} + \frac{4}{3 x - 3}$

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

Jun 18, 2017

color(green)((2x^2+2x-2)+4/(3x-3)

#### Explanation:

$\left(6 {x}^{3} - 12 x + 10\right) \div \left(3 x - 3\right)$

 color(white)(.............)ul(color(green)(2x^2+2x-2)
$\textcolor{w h i t e}{a} 3 x - 3$$|$$6 {x}^{3} + 0 - 12 x + 10$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots} \underline{6 {x}^{3} - 6 {x}^{2}}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots} 6 {x}^{2} - 12 x$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots} \underline{6 {x}^{2} - 6 x}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots} - 6 x + 10$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} \underline{- 6 x + 6}$
color(white)(.......................................)color(green)(+4

 color(white)(.............)color(green)((2x^2+2x-2)+4/(3x-3)