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Math Help - Galois group

  1. #1
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    Galois group

    I'm asked to find the Galois group of this polynomial over Q:
    x^5-2x^3-x^2+2.

    This is irreducible over Q, but over Fp where p is prime, the polynomial factorises. Does this information help, or is there a different way to find the Galois group?
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  2. #2
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    Quote Originally Posted by KSM08 View Post
    I'm asked to find the Galois group of this polynomial over Q:
    x^5-2x^3-x^2+2.

    This is irreducible over Q, but over Fp where p is prime, the polynomial factorises. Does this information help, or is there a different way to find the Galois group?

    x^5-2x^3-x^2+2=(x-1)(x^4+x^3-x^2-2x-2)\Longrightarrow your polynomial is reducible over \mathbb{Q} .

    Tonio
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