= Square-free polynomial
{title2=$p=c\prod_i f_i\quad(f_i\text{ distinct monic irreducibles})$}
= Squarefree polynomial
{synonym}
A nonzero <polynomial> over a <field> is square-free if no square of a nonconstant <irreducible polynomial> divides it. Equivalently, in its <factorization of polynomials>, every <irreducible polynomial> factor occurs with exponent one. For example, $x(x^2+1)$ is square-free over the <real numbers>, whereas $(x-1)^2$ is not. Square-freeness over a given <field> concerns factors in that <field>; over the <real numbers> or <complex numbers>, it is equivalent to having no repeated <polynomial roots> after splitting over the <complex numbers>.
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