# How do I use the remainder theorem to divide 2x^2-5x-1 by x-4?

Feb 28, 2016

$2 x + 3 + \frac{11}{x - 4}$

#### Explanation:

I used synthetic division to solve this, but you can use long division too, if you like.

$\textcolor{w h i t e}{4.} |$$\textcolor{w h i t e}{.} 2 \textcolor{w h i t e}{. .} - 5 \textcolor{w h i t e}{. .} - 1$
$4 \textcolor{w h i t e}{.} |$_____

This becomes
$\textcolor{w h i t e}{4.} |$$\textcolor{w h i t e}{.} 2 \textcolor{w h i t e}{. .} - 5 \textcolor{w h i t e}{. .} - 1$
$4 \textcolor{w h i t e}{.} |$__$8$____$12$_
$\textcolor{w h i t e}{4. \ldots} \textcolor{b l u e}{2}$$\textcolor{w h i t e}{4. \ldots .} \textcolor{g r e e n}{3}$$\textcolor{w h i t e}{4. \ldots} \textcolor{red}{11}$

This is rewritten as $\textcolor{b l u e}{2} x + \textcolor{g r e e n}{3} + \frac{\textcolor{red}{11}}{x - 4}$