# How do you find the quotient of (x^3+11x+14)div (x+2) using long division?

Aug 25, 2017

color(magenta)((x^3+11x+14) / (x+2) = x^2-2x+15 and remainder of color(magenta)((-16)/(x+2)

#### Explanation:

$\textcolor{w h i t e}{\ldots \ldots \ldots .} \textcolor{w h i t e}{.} \underline{{x}^{2} - 2 x + 15}$
$x + 2 | {x}^{3} + 0 + 11 x + 14$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots} \underline{{x}^{3} + 2 {x}^{2}}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots} - 2 {x}^{2} + 11 x$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} \underline{- 2 {x}^{2} - 4 x}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots} 15 x + 14$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots} \underline{15 x + 30}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} - 16$

color(magenta)((x^3+11x+14) / (x+2) = x^2-2x+15 and remainder of color(magenta)((-16)/(x+2)