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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
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    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
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  3. #3
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    Re: Factorization

    Hello, MoniMini!

    Another approach . . .



    \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}
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