# How do you divide (x^4+2x^3+ 5 x^2-4x-2)/(x+2) ?

Apr 20, 2017

${x}^{3} + 5 x - 14 + \frac{26}{x + 2}$

#### Explanation:

I'd like to use synthetic division for $\textcolor{red}{1} {x}^{4} + \textcolor{b l u e}{2} {x}^{3} + \textcolor{p u r p \le}{5} {x}^{2} + \textcolor{g r e e n}{- 4} x + \textcolor{\mathmr{and} a n \ge}{- 2}$

$\textcolor{b l a c k}{- 2} \textcolor{b l a c k}{|} \textcolor{red}{1} \textcolor{w h i t e}{-} \textcolor{b l u e}{2} \textcolor{w h i t e}{-} \textcolor{p u r p \le}{5} \textcolor{w h i t e}{.} \textcolor{g r e e n}{- 4} \textcolor{w h i t e}{.} \textcolor{\mathmr{and} a n \ge}{- 2}$
$\textcolor{w h i t e}{- 2} \textcolor{b l a c k}{|} \textcolor{w h i t e}{1} \textcolor{w h i t e}{.} \textcolor{b l a c k}{- 2} \textcolor{w h i t e}{-} \textcolor{b l a c k}{0} \textcolor{w h i t e}{.} \textcolor{b l a c k}{- 10} \textcolor{w h i t e}{.} \textcolor{b l a c k}{28}$
$\textcolor{w h i t e}{- 2.} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$
$\textcolor{w h i t e}{- 2} \textcolor{b l a c k}{|} \textcolor{b l a c k}{1} \textcolor{w h i t e}{-} \textcolor{b l a c k}{0} \textcolor{w h i t e}{-} \textcolor{b l a c k}{5} \textcolor{w h i t e}{.} \textcolor{b l a c k}{- 14} \textcolor{w h i t e}{.} \textcolor{b l a c k}{26}$

We have a remainder, but that's not a problem :)

${x}^{3} + 0 {x}^{2} + 5 x - 14 + \frac{26}{x + 2}$
${x}^{3} + 5 x - 14 + \frac{26}{x + 2}$