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Math Help - Factorization

  1. #1
    Junior Member MoniMini's Avatar
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    Post 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
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Factorization

    Do you mean:

    x^3+x^{-3}-2 ?
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  3. #3
    Junior Member MoniMini's Avatar
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    Re: 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"
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Factorization

    I'm still not sure if I interpreted your original post correctly, but if I did, then I would write:

    \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 x^3? How can you factor this?
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