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

Feb 15, 2017

$2 {x}^{2} + 2 x - 1 + \frac{4}{x - 2}$

#### Explanation:

One way is to express the numerator as factors of the divisor (x-2)

$\textcolor{red}{2 {x}^{2}} \left(x - 2\right) + \left(\textcolor{b l u e}{+ 4 {x}^{2}} - 2 {x}^{2}\right) - 5 x + 6$

$= \textcolor{red}{2 {x}^{2}} \left(x - 2\right) \textcolor{red}{+ 2 x} \left(x - 2\right) + \left(\textcolor{b l u e}{+ 4 x} - 5 x\right) + 6$

$= \textcolor{red}{2 {x}^{2}} \left(x - 2\right) \textcolor{red}{+ 2 x} \left(x - 2\right) \textcolor{red}{- 1} \left(x - 2\right) + \left(\textcolor{b l u e}{- 2} + 6\right)$

$\Rightarrow \frac{2 {x}^{3} - 2 {x}^{2} - 5 x + 6}{x - 2}$

$= \textcolor{red}{2 {x}^{2} + 2 x - 1} + \frac{4}{x - 2}$