# Math Help - [SOLVED] Dividing Polymonials by Polynomials

1. ## [SOLVED] Dividing Polymonials by Polynomials

I am stuck with these. No idea how to do them. Here is my first problem:

x^3+x^2y+xy^2+y^3 / x+y

I don't want an answer. I want an explanation on how to do it.

2. Originally Posted by Taelord
I am stuck with these. No idea how to do them. Here is my first problem:

x^3+x^2y+xy^2+y^3 / x+y

I don't want an answer. I want an explanation on how to do it.
You can do it by long division, or you could simply note:
$x^3+x^2y+xy^2+y^3$

$= (x^3 + x^2y) + (xy^2 + y^3)$

$= x^2(x + y) + y^2(x + y)$

$= (x^2 + y^2)(x + y)$

Thus
$\frac{x^3+x^2y+xy^2+y^3}{x + y} = x^2 + y^2$

Since this is a division of a linear polynomial in x you could also rig a synthetic division for it.

-Dan