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Homework Help: Is the polynomial irreducible

  1. Apr 2, 2014 #1
    1. The problem statement, all variables and given/known data
    Is [tex]f(x)=x^2+1[/tex] irreducible in [tex]\mathbb{F}_2[x][/tex]
    If not then factorise the polynomial.




    3. The attempt at a solution

    [tex]\mathbb{F}_2[x]=\{0,1\}[/tex]
    [tex]f(0)=1[/tex]
    [tex]f(1)=1+1=0[/tex]
    Hence the polynomial is not irreducible
     
  2. jcsd
  3. Apr 2, 2014 #2
    solved do not bother answering
     
  4. Apr 2, 2014 #3

    Mark44

    Staff: Mentor

    Looks good.
     
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