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
Hello, MoniMini!
Another approach . . .
$\displaystyle \text{Factor: }\: x^3 + x^{-3} - 2$
We have: .$\displaystyle x^3 - 2 + \frac{1}{x^3} \;=\;\frac{x^6 - 2x^3 + 1}{x^3} \;=\;\frac{(x^3-1)^2}{x^3}$
. . . . . . . $\displaystyle =\;\frac{[(x-1)(x^2+x+1)]^2}{x^3} \;=\; \frac{(x-1)^2(x^2+x+1)^2}{x^3}$