# How do you find the quotient of (m^4-2m^3+m^2+12m-6)/(m-2) using synthetic division?

Jan 31, 2018

Quotient $\textcolor{g r e e n}{Q = {m}^{2} + m + 14}$, Remainder $\textcolor{g r e e n}{R = \frac{22}{m - 2}}$

#### Explanation:

$\textcolor{w h i t e}{a a} 2 \textcolor{w h i t e}{a a} | \textcolor{w h i t e}{a a} 1 \textcolor{w h i t e}{a a} - 2 \textcolor{w h i t e}{a a} 1 \textcolor{w h i t e}{a a} 12 \textcolor{w h i t e}{a a} - 6$
$\textcolor{w h i t e}{a a a a a} | \textcolor{w h i t e}{a} \downarrow \textcolor{w h i t e}{a a a a} 2 \textcolor{w h i t e}{a a} 0 \textcolor{w h i t e}{a a a} 2 \textcolor{w h i t e}{a a a} 28$
$\textcolor{w h i t e}{a a a a a} - - - - - - - - - -$
$\textcolor{w h i t e}{a a a a a a a a a} 1 \textcolor{w h i t e}{a a a a} 0 \textcolor{w h i t e}{a a} 1 \textcolor{w h i t e}{a a a} 14 \textcolor{w h i t e}{a a a} 22$

Quotient $\textcolor{g r e e n}{Q = {m}^{2} + m + 14}$, Remainder $\textcolor{g r e e n}{R = \frac{22}{m - 2}}$