Not sure if im going mad but struggling with this (Thinking)

(a) Write down the polynomial P in x, y such that:

x^6 − y^6 = (x^2 − y^2)*P.

Many thanks in advance.

Printable View

- January 25th 2011, 05:43 AMbreitlingPloynomial...
Not sure if im going mad but struggling with this (Thinking)

(a) Write down the polynomial P in x, y such that:

x^6 − y^6 = (x^2 − y^2)*P.

Many thanks in advance.

- January 25th 2011, 05:59 AMFernandoRevilla
:__Hint__

Denote and then,

so,

is a root of

and you can decompose it using Ruffini's rule.

Fernando Revilla - January 25th 2011, 06:10 AMSoroban
Hello, breitling!

Quote:

. .

Don't you recognize that*difference of cubes?*

. . . .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The very least you can do is some Long Division . . .

. .

- January 25th 2011, 07:32 AMProve It
A better solution:

by the Difference of Two Cubes rule...

.

So what is ? - January 31st 2011, 05:03 AMbreitling
The question actually asked x^6-y^6=(x^2+y^2)*p got the sign wrong.

- January 31st 2011, 05:25 AMHallsofIvy