# How do you divide (7x^4 -5x^3-5x^2+x-2)/((x + 4) )?

Jan 18, 2017

$7 {x}^{3} - 33 {x}^{2} + 127 x + 507 - \frac{2030}{x + 4}$

#### Explanation:

$\text{ } 7 {x}^{4} - \textcolor{w h i t e}{2} 5 {x}^{3} - 5 {x}^{2} + x - 2$
$\textcolor{red}{7 {x}^{3}} \left(x + 4\right) \to \underline{7 {x}^{4} + 28 {x}^{3}} \leftarrow \text{ subtract}$
$\text{ } 0 \textcolor{w h i t e}{{x}^{2}} - 33 {x}^{3} - \textcolor{w h i t e}{13} 5 {x}^{2} + x - 2$
$\textcolor{red}{- 33 {x}^{2}} \left(x + 4\right) \to \underline{\textcolor{w h i t e}{.} - 33 {x}^{3} - 132 {x}^{2}} \leftarrow \text{ subtract}$
$\text{ "0+ 127x^2+" } x - 2$
color(red)(127x)(x+4)->ul(" "127x^2+508x) larr" subtract"
$\text{ } 0 - 507 x - \textcolor{w h i t e}{202} 2$
color(red)(507)(x+4)->ul(" " -507x+2028 ) larr" sub."
$\text{ "0" } \textcolor{g r e e n}{- 2030}$

The $\textcolor{g r e e n}{- 2030}$ is a remainder so putting it all together we have:

$\textcolor{red}{7 {x}^{3} - 33 {x}^{2} + 127 x + 507} \textcolor{g r e e n}{- \frac{2030}{x + 4}}$