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Math Help - Eisenstein Criterium

  1. #1
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    Eisenstein Criterium

    Investigate if f is irreducible in Q[X] and Z[X]:

    i) f=2X^5-6X^3+9X^2-15
    ii) f=3X^4+6X^2+6

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  2. #2
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    Quote Originally Posted by roporte View Post
    i) f=2X^5-6X^3+9X^2-15
    ii) f=3X^4+6X^2+6
    Irreducibility in Z and Q are equivalent by Gauss' lemma. Now in (i) let p=3 then p divides -6,9,-15 by p^2 does not divide -15 and so it is irreducible. In (ii) let p=2 then p divides 6 and 6 but p^2 does not divide 6.
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