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

Apr 12, 2017

${x}^{2} + 4 x + 5 + \frac{5}{x - 2}$

#### Explanation:

One way is to use the divisor x - 2 as a factor in the numerator.

$\text{Consider the numerator}$

$\textcolor{red}{{x}^{2}} \left(x - 2\right) \textcolor{red}{+ 2 {x}^{2}} + 2 {x}^{2} - 3 x - 5$

$= \textcolor{red}{{x}^{2}} \left(x - 2\right) \textcolor{red}{+ 4 x} \left(x - 2\right) \textcolor{red}{+ 8 x} - 3 x - 5$

$= \textcolor{red}{{x}^{2}} \left(x - 2\right) \textcolor{red}{+ 4 x} \left(x - 2\right) \textcolor{red}{+ 5} \left(x - 2\right) \textcolor{red}{+ 10} - 5$

$= \textcolor{red}{{x}^{2}} \left(x - 2\right) \textcolor{red}{+ 4 x} \left(x - 2\right) \textcolor{red}{+ 5} \left(x - 2\right) + 5$

$\Rightarrow \frac{{x}^{3} + 2 {x}^{2} - 3 x - 5}{x - 2} = \textcolor{red}{{x}^{2} + 4 x + 5} + \frac{5}{x - 2}$

$\text{quotient is " x^2+4x+5" and remainder } = 5$