Hey!!

In my notes there is the following:

Let $F$ be a field. The irresducible $f\in F[x]$ is separable, if all the roots are different.

A non-constant polynomial $f\in K[x]$ is separable, if all the irreducible factors are separable.

Example:

$f(x)=(x^2-2)^2(x^2+3)\in \mathbb{Q}[x]$.

The irreducible factors are:

- $x^2-2$ $\rightarrow$ Roots : $\pm 2$ different
- $x^2+3$ $\rightarrow$ Roots : $\pm i\sqrt{3}$ different

So, $f$ is separable.

I haven't understood why $f$ is separable. Since we have the factor $(x^2-2)^2$ aren't the roots $\pm 2$ of multiplicity $2$ ?