# Factorization

• May 13th 2013, 11:04 PM
MoniMini
Factorization
Hi there!
How does one factorize $x^3 + (x^-3) - 2$?
I tried factorizing it by $x^3 - 1 + (x^-3) -1$ and a few other methods
but couldn't really get close to the answer.

Thanks
• May 13th 2013, 11:42 PM
ibdutt
Re: Factorization
let x^3 = a
The equation becomes a + 1/a -2 = 0
a^2 - 2a + 1 = 0 That gives ( a -1 )^2 = 0 OR ( x^3 - 1 )^2 = 0
and we know the factors of x^3 - 1
• May 14th 2013, 07:22 AM
Soroban
Re: Factorization
Hello, MoniMini!

Another approach . . .

Quote:

$\text{Factor: }\: x^3 + x^{-3} - 2$

We have: . $x^3 - 2 + \frac{1}{x^3} \;=\;\frac{x^6 - 2x^3 + 1}{x^3} \;=\;\frac{(x^3-1)^2}{x^3}$

. . . . . . . $=\;\frac{[(x-1)(x^2+x+1)]^2}{x^3} \;=\; \frac{(x-1)^2(x^2+x+1)^2}{x^3}$