Thread: Factorization of the polynomial

I need to factor the next polynomial:

Originally Posted by Aero763

I need to factor the next polynomial:

For a start, it's not a polynomial. But it is possible to simplify it. As a hint, let and , and express everything in terms of x and y.

Since which is the denominator, you can factor the numerator as a sum of perfect cubes.

Originally Posted by Krizalid

Since which is the denominator, you can factor the numerator as a sum of perfect cubes.

Thank you, but I already tried that to no avail.

Originally Posted by Opalg

For a start, it's not a polynomial. But it is possible to simplify it. As a hint, let and , and express everything in terms of x and y.

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?

Opalg's hint is just to make things easier to work, haha, you coulda solved the problem directly, with no substitutions.

You are right, I can see it now!