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
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
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