# How do you simplify and divide (x^5-7x^3+x+1)/(x+3)?

##### 1 Answer
Jan 20, 2017

${x}^{4} - 3 {x}^{3} + 2 {x}^{2} - 6 x + 13$ and remainder of-38

#### Explanation:

$\textcolor{w h i t e}{a a a a a a a a a a}$${x}^{4} - 3 {x}^{3} + 2 {x}^{2} - 6 x + 13$
$\textcolor{w h i t e}{a a a a a a a a a a}$$- - - - - - - - -$
$\textcolor{w h i t e}{a a a a} x - 4$$|$${x}^{5} + 0 - 7 {x}^{3} + 0 + x + 1$
$\textcolor{w h i t e}{a a a a a a a a a a}$${x}^{5} + 3 {x}^{4}$color(white)
$\textcolor{w h i t e}{a a a a a a a a a a a}$$0 - 3 {x}^{4} - 7 {x}^{3}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$- 3 {x}^{4} - 9 {x}^{3}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a a a a a}$$2 {x}^{3} + 0$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a a a a a}$$2 {x}^{3} + 6 {x}^{2}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a a a a a a a a}$$- 6 {x}^{2} + x$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a a a a a a a a}$$- 6 {x}^{2} - 12 x$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a}$$13 x + 1$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a}$$13 x + 39$