Is $f=t^5 + t^4 + 1$ reducible or irreducible over the field of $Z_2$ integers modulo 2.

Question

I need to find out whether $f=t^5 + t^4 + 1$ is reducible or irreducible over the field of $Z_2$ integers modulo 2. I approached the question by substituting 0 and 1 into the function and got answers which were not equal to 0. Hence I assumed that the function is irreducible over the field of $Z_2$ integers modulo 2, because it does not have a root. Is this approach and answer right?