How can we show that the polynomial $f(x)=1+x+x^3+x^4$ is not irreducible over any field?
-1 is an element of every field and is also a root of $f(x)$. Thus $x+1$ divides $f(x)$ and so $f(x)$ is not irreducible.
Sign up using Google
Sign up using Facebook
Sign up using Stack Exchange
3 years ago