Hi there!

How does one factorize $\displaystyle x^3 + (x^-3) - 2$?

I tried factorizing it by $\displaystyle x^3 - 1 + (x^3) -1$ and a few other methods

but couldn't really get close to the answer.

Thanks

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- May 13th 2013, 10:49 PMMoniMiniFactorization
Hi there!

How does one factorize $\displaystyle x^3 + (x^-3) - 2$?

I tried factorizing it by $\displaystyle x^3 - 1 + (x^3) -1$ and a few other methods

but couldn't really get close to the answer.

Thanks - May 13th 2013, 11:02 PMMarkFLRe: Factorization
Do you mean:

$\displaystyle x^3+x^{-3}-2$ ? - May 14th 2013, 12:12 AMMoniMiniRe: Factorization
Yeah, I actually don't know how to write mathematical formulae on the website.

All I mean is "x cube plus one upon x cube minus 2" - May 14th 2013, 12:26 AMMarkFLRe: Factorization
I'm still not sure if I interpreted your original post correctly, but if I did, then I would write:

$\displaystyle \frac{x^6-2x^3+1}{x^3}=\frac{(x^3)^2-2x^3+1}{x^3}$

Do you see now how the numerator is a quadratic in $\displaystyle x^3$? How can you factor this?