Is x^2+1 Irreducible Over Finite Field F_2?

[jimmycricket]

Homework Statement

Is f(x)=x^2+1 irreducible in \mathbb{F}_2[x]
If not then factorise the polynomial.

The Attempt at a Solution

\mathbb{F}_2[x]=\{0,1\}
f(0)=1
f(1)=1+1=0
Hence the polynomial is not irreducible

 

[jimmycricket]

solved do not bother answering

 

[Mark44]

Homework Statement

Is f(x)=x^2+1 irreducible in \mathbb{F}_2[x]
If not then factorise the polynomial.

The Attempt at a Solution

\mathbb{F}_2[x]=\{0,1\}
f(0)=1
f(1)=1+1=0
Hence the polynomial is not irreducible

Looks good.