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Factorisation of cyclotomic polynomials

  1. Mar 18, 2007 #1
    x^16 + 1 is irreducible over the rationals, correct?.......

    .........also I am required to factorise the following polynomials

    2) i) x^5 + 3x^4 + 2x^3 + x^2 -7

    ii) x^5 + 10x^4 + 13x^3 -25x^2 -68x -60

    now I would usually approach this using the factor theorem to find a factor and then divide by this factor and continue, however in the question I am told as a hint that I am to try substituting x-> x+h h=+-1, +-2, why all this is necessary i canot think?.....
    Last edited: Mar 18, 2007
  2. jcsd
  3. Mar 19, 2007 #2

    Gib Z

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    Homework Helper

    "x^16 + 1 is irreducible over the rationals, correct?......."


    As for your hint, that is usually used to alter the roots of an equation. eg of the roots of a polynomial of degree 3 in x, is alpha, beta and gamma, subbing in x+1 will get you a polynomial that has roots alpha-1, beta -1 , gamma -1 etc etc.

    Maybe thats a hint your ment to use creatively?
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