Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a square-free polynomial is a polynomial with no square factors, i.e, f in F[x] is square-free if and only if b^2 nmid f for every b in F[x] with non-zero degree. This definition implies that no factors of higher order can exist, either, for if b3 divided the polynomial, then b2 would divide it also. In applications in physics and engineering, a square-free polynomial is much more commonly called a polynomial with no repeated roots. Any separable polynomial is square-free. Conversely, if the field F is perfect, all square-free polynomials over F are separable. In particular, if f is a square-free polynomial over a perfect field, then the greatest common divisor of f and its formal derivative f ? is 1. A square-free factorization of a polynomial is a factorization into powers of square-free factors, i.e: f(x) = a_1(x) a_2(x)^2 a_3(x)^3 cdots a_n(x)^n where the ak(x) are pairwise coprime square-free polynomials.

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