1. ## [SOLVED] Polynomial question

Hi, this is probably quite a simple question, but i am stuck, and can't find anything like it in the lecture notes, so your help will be appreciated.

the question is
Write down the polynomial P in x,y such that that x^4 - x^4 = (x-y)P

Explanations with answers will really help me too! Thanks

2. Originally Posted by Rapid_W
Hi, this is probably quite a simple question, but i am stuck, and can't find anything like it in the lecture notes, so your help will be appreciated.

the question is
Write down the polynomial P in x,y such that that x^4 - x^4 = (x-y)P

Explanations with answers will really help me too! Thanks
x^4-x^4 = 0 . Sure you didn't mean x^4-y^4?

If so x^4-y^4 is the difference of two squares:

$\displaystyle x^4-y^4 = (x^2-y^2)(x^2+y^2)$

However, x^2-y^2 is also the difference of two squares

$\displaystyle x^4-y^4 = (x-y)(x+y)(x^2+y^2)$

which gives $\displaystyle P = (x+y)(x^2+y^2) = x^3 + xy^2 + x^2y + y^3$

3. Yes, i did mean that sorry! Thanks very much for the answer