I need to factor the next polynomial:

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- Aug 1st 2011, 09:26 AMAero763Factorization of the polynomial
I need to factor the next polynomial:

- Aug 1st 2011, 11:29 AMOpalgRe: Factorization of the polynomial
- Aug 1st 2011, 11:51 AMKrizalidRe: Factorization of the polynomial
Since which is the denominator, you can factor the numerator as a sum of perfect cubes.

- Aug 1st 2011, 10:12 PMAero763Re: Factorization of the polynomial
Thank you, but I already tried that to no avail.

Thank you, that worked like a charm! I already came up with the idea, but was not sure what to do with in the denominator. But since you suggested it, I took a closer look and sure enough - it worked!

There how it goes:

1) First we need to do something with , which confused me, when I tried to solve it by myself. We need to get it in the form of and somehow. Well, is equal to , and we can add and substract 1. Therefore:

Here we go

Now, let and , and express everything in terms of x and y:

By definition , and , therefore:

Simplify:

And the answer is:

Thank you guys again, been trying to solve this tough cookie for a couple of days now.

P.S. if it is not a polynomial, then what is it? - Aug 1st 2011, 10:19 PMKrizalidRe: Factorization of the polynomial
Opalg's hint is just to make things easier to work, haha, you coulda solved the problem directly, with no substitutions.

- Aug 1st 2011, 10:27 PMAero763Re: Factorization of the polynomial
You are right, I can see it now!