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.