Square-free polynomial

In mathematics, a square-free polynomial is a polynomial defined over a field (or more generally, a unique factorization domain) that does not have as a factor any square of a non-unit factor. In the important case of univariate polynomials over a field k, this means that, ${\displaystyle f\in k[X]}$ is square-free if and only if ${\displaystyle b^{2}\nmid f}$ for every polynomial ${\displaystyle b\in k[X]}$ of positive degree. In applications in physics and engineering, a square-free polynomial is commonly called a polynomial with no repeated roots. Such polynomials are called separable, but over a perfect field being separable is the same as being square-free.

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