Polynomial Division: Simplifying with Long Division

[chris92]

1. Hi I have a question I am stuck on it is:

(x³ + 2x²y - 2xy² - y³)/(x-y)

Can anyone help?

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

What do you mean by "help"? What help do you need or want? You title this "long hand polynomial division" (I would have said just "polynomial division"- "long hand" makes me think of cursive writing!) so apparently you know what you are supposed to do. How many times does x divide into $x^3$? What do you do next?

 

[Ray Vickson]

1. Hi I have a question I am stuck on it is:
x³+2x²y-2xy²-y³/x - y

Can anyone help?

Homework Equations

The Attempt at a Solution

What you have written is not a polynomial; it is a rational function of the form
$$x^3 + 2 x^2 y -2xy^2 - \frac{y^3}{x}-y.$$ Did you intend to write
$$\frac{x^3 + 2x^2y-2xy^2-y^3}{x-y} ?$$
If that is what you meant you should have used parentheses, like this:
(x³ + 2x²y - 2xy² - y³)/(x-y).

 

[chris92]

Hi yes that is what I meant sorry .

 

[LeonhardEu]

there is more in wikipedia too. Since this is a simple example i think you should check the basics of polynomial division. It's nothing too difficult, it simply requires a little practice.

 

[berkeman]

@chris92 -- check your PMs, and then show your work on your problem here in this thread.

 

[LCKurtz]

@chris92: Are you required to do long division? There is a much easier way to simplify it.

Edit: Woops, maybe not. I had a sign wrong...