# How do you divide ( -14x^2 + 4x^2 + 19 +4x)/(2x-5)?

Jan 4, 2018

color(magenta)( (-14x^3+4x^2+4x+19)/(2x-5) = -7x^2-15.5x-36.75 and remainder color(magenta)(-164.75/(2x-5)

#### Explanation:

$\frac{- 14 {x}^{2} + 4 {x}^{2} + 19 + 4 x}{2 x - 5}$

I think$- 14 {x}^{2}$ should be $- 14 {x}^{3}$

$\therefore = \frac{- 14 {x}^{3} + 4 {x}^{2} + 4 x + 19}{2 x - 5}$

$\textcolor{w h i t e}{\ldots \ldots} \textcolor{w h i t e}{\ldots \ldots} - 7 {x}^{2} - 15.5 x - 36.75$
$2 x - 5 | \overline{- 14 {x}^{3} + 4 {x}^{2} + 4 x + 19}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} \underline{- 14 {x}^{3} + 35 {x}^{2}}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots .} - 31 {x}^{2} + 4 x$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} \underline{- 31 {x}^{2} + 77.5 x}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} - 73.5 x + 19$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots} \underline{- 73.5 x + 183.75}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots} - 164.75$

color(magenta)( (-14x^3+4x^2+4x+19)/(2x-5) = -7x^2-15.5x-36.75 and remainder color(magenta)(-164.75/(2x-5)