# How do you divide (2x^3+2x^2+4x+4)/(x^2+8x+4)?

Aug 8, 2018

$\frac{\textcolor{b l u e}{2 {x}^{3} + 2 {x}^{2} + 4 x + 4}}{\textcolor{red}{{x}^{2} + 8 x + 4}} = \textcolor{g r e e n}{\left(2 x - 14\right)} + \frac{108 x + 60}{\textcolor{red}{{x}^{2} + 8 x + 4}}$

#### Explanation:

Here ,

Dividend $: \textcolor{b l u e}{2 {x}^{3} + 2 {x}^{2} + 4 x + 4} \mathmr{and}$

divisor $: \textcolor{red}{{x}^{2} + 8 x + 4}$

So ,

color(white)(..................................)color(green)(ul(2x-14color(white)(.........))larrquotient
$\textcolor{w h i t e}{\ldots \ldots \ldots .} \textcolor{red}{\left({x}^{2} + 8 x + 4\right)}$ $| \textcolor{b l u e}{2 {x}^{3} + 2 {x}^{2} + 4 x + 4}$ 

color(white)()color(violet)((color(red)(x^2+8x+4))*2xtocolor(white)()ul(2x^3+16x^2+8x)$\textcolor{w h i t e}{\ldots \ldots .} \Leftarrow \text{subtract}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} - 14 {x}^{2} - 4 x + 4$

color(white)()color(violet)((color(red)(x^2+8x+4))(-14)tocolor(white)()ul(-14x^2-112x-56)$\textcolor{w h i t e}{\ldots \ldots .} \Leftarrow \text{subtract}$
color(white)(..........................................)color(green)($\textcolor{w h i t e}{\ldots \ldots \ldots} 108 x + 60 \leftarrow \text{Remainder}$

Hence ,

$\left(\textcolor{b l u e}{2 {x}^{3} + 2 {x}^{2} + 4 x + 4}\right)$=$\left(\textcolor{red}{{x}^{2} + 8 x + 4}\right) \left(2 x - 14\right) + \left(108 x + 60\right)$

Quotient :q(x)=color(green)(2x-14 $\text{and Remainder } : r \left(x\right) = 108 x + 60$