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Built-in Mathematica Symbol

FactorSquareFree

FactorSquareFree[poly]
pulls out any multiple factors in a polynomial.

FactorSquareFree[poly, Extension->Automatic] extends the coefficient field to include algebraic numbers that appear in the coefficients of poly.

FactorSquareFree automatically threads over lists, as well as equations, inequalities and logic functions.

Pull out multiple factors:

A complete factorization:

Pull out multiple factors:

A complete factorization:

A univariate polynomial:

A multivariate polynomial:

A rational function:

By default algebraic number coefficients are treated as independent variables:

With Extension->Automatic algebraic dependencies between coefficients are recognized:

Pull out multiple factors over the integers modulo 2:

Pull out multiple factors in a trigonometric expression:

FactorSquareFree only pulls out multiple factors:

Factor gives a complete factorization:

Expand is effectively the inverse of FactorSquareFree:

FactorSquareFreeList gives a list of factors:

A univariate polynomial has multiple factors if an only if its Discriminant is zero: