A polynomial over a field is separable when it has no repeated root in a splitting field. Equivalently, it is coprime to its formal derivative.
A separable polynomial is a polynomial that does not have repeated roots in its splitting field. More formally, a polynomial \( f(x) \) over a field \( K \) is termed separable if its derivative \( f'(x) \) and \( f(x) \) share no common roots in an algebraic closure of \( K \).
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