# How do you divide (2x^2 -7x+ 19) div(2x- 3)?

Oct 27, 2016

"How do you" type questions are answered by explanation.

#### Explanation:

I use long division:

I am going to use the square root symbol, because I do not find a long division symbol in formatter but please read it as division:

$\textcolor{w h i t e}{_} \textcolor{w h i t e}{_} \textcolor{w h i t e}{_} \textcolor{w h i t e}{_} x - 2$
$2 x - 3 \sqrt{2 {x}^{2} - 7 x + 19}$
$\textcolor{w h i t e}{_} \textcolor{w h i t e}{-} - 2 {x}^{2} + 3 x$
$\textcolor{w h i t e}{_} \textcolor{w h i t e}{_} \textcolor{w h i t e}{.} \textcolor{w h i t e}{_} 0 - 4 x + 19$
$\textcolor{w h i t e}{_} \textcolor{w h i t e}{_} \textcolor{w h i t e}{_} \textcolor{w h i t e}{_} \textcolor{w h i t e}{_} 4 x - 6$
$\textcolor{w h i t e}{_} \textcolor{w h i t e}{_} \textcolor{w h i t e}{_} \textcolor{w h i t e}{_} \textcolor{w h i t e}{_} 0 + 13$

The quotient is $x - 2$ with remainder 13

Written as a mixed number:

$x - 2 + \frac{13}{2 x - 3}$