# How do you divide ( x^3 + x^2 + 4x + 4 )/(x - 2 )?

Jul 9, 2016

${x}^{2} + 3 x + 10 + \frac{24}{x - 2}$

#### Explanation:

$\textcolor{w h i t e}{. .}$

$\text{ } {x}^{3} + {x}^{2} + 4 x + 4$
$\textcolor{red}{+ {x}^{2}} \left(x - 2\right) \to \textcolor{w h i t e}{.} \underline{{x}^{3} - 2 {x}^{2}} \text{ "larr" Subtract}$
$\text{ } 0 \textcolor{w h i t e}{.} + 3 {x}^{2} + 4 x + 4$
$\textcolor{red}{+ 3 x} \left(x - 2\right) \to \text{ "color(white)(.)ul(3x^2-6x)" "larr" Subtract}$
$\text{ } 0 + 10 x + 4$
$\textcolor{red}{+ 10} \left(x - 2\right) \to \text{ "ul(10x-20)" "larr" Subtract}$
" "color(red)(0+24" "larr" Remainder")

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\left({x}^{3} + {x}^{2} + 4 x + 4\right) \div \left(x - 2\right) \text{ "color(red)(=" } {x}^{2} + 3 x + 10 + \frac{24}{x - 2}$