# Is the polynomial irreducible

1. Apr 2, 2014

### jimmycricket

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

3. 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

2. Apr 2, 2014