Every irreducible polynomial over a perfect field is separable. A polynomial over a perfect field is separable if and only if it is a product of distinct irreducible polynomials.

What are separable and inseparable extensions?

A polynomial such as this one, whose formal derivative is zero, is said to be inseparable. Polynomials that are not inseparable are said to be separable. A separable extension is an extension that may be generated by separable elements, that is elements whose minimal polynomials are separable.

Are irreducible polynomials Monic?

Among the polynomials of which x is a root, there is exactly one which is monic and of minimal degree, called the minimal polynomial of x. The minimal polynomial of an algebraic element x of L is irreducible, and is the unique monic irreducible polynomial of which x is a root.