Show that $f(x) = 2x^2+4$ is reducible over $\mathbb{C}$ I know that this question has already been asked here before, but there's just one part that I didn't get. By definition a polynomial is irreducible whenever we can write $f(x) = g(x)h(x)$ and $g(x)$ or $h(x)$ is a unit. In our case we have
$f(x) = 2(x^2+2)$, but $2$ is a unit over $\mathbb{C}$, right? so why is $f(x)$ reducible? Am I using the right definition?

Hint
$$x^2+2=x^2-(i\sqrt{2})^2$$
