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FactorSquareFreeList[poly]

gives a list of square‐free factors of a polynomial, together with their exponents.

Examples  
Basic Examples  
Scope  
Options  
Extension  
Modulus  
Trig  
Applications  
Properties & Relations  
See Also
Tech Notes
Related Guides
History
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FactorSquareFreeList

FactorSquareFreeList[poly]

gives a list of square‐free factors of a polynomial, together with their exponents.

Examples

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Basic Examples  (2)

List square-free factors of a polynomial:

List irreducible factors of a polynomial:

Scope  (8)

A univariate polynomial:

A multivariate polynomial:

A rational function:

A polynomial with complex coefficients:

Non-polynomial expressions:

Square-free factors of a polynomial over the integers modulo 3:

Square-free factors of a polynomial over a finite field:

Compute the square-free factorization of a polynomial of degree :

Options  (4)

Extension  (2)

By default algebraic number coefficients are treated as independent variables:

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

Modulus  (1)

Find square-free factors over the integers modulo 2:

Trig  (1)

List multiple factors in a trigonometric expression:

Applications  (1)

Remove root multiplicities:

Properties & Relations  (3)

FactorSquareFreeList gives a list of square-free factors:

This multiplies the factors together:

FactorSquareFree gives a product of factors:

Expand combines all the factors back together:

FactorList gives a list of irreducible factors:

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

FactorInteger gives a list of prime factors of an integer:

Wolfram Research (1988), FactorSquareFreeList, Wolfram Language function, https://reference.wolfram.com/language/ref/FactorSquareFreeList.html (updated 2023).

Text

Wolfram Research (1988), FactorSquareFreeList, Wolfram Language function, https://reference.wolfram.com/language/ref/FactorSquareFreeList.html (updated 2023).

CMS

Wolfram Language. 1988. "FactorSquareFreeList." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/FactorSquareFreeList.html.

APA

Wolfram Language. (1988). FactorSquareFreeList. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FactorSquareFreeList.html

BibTeX

@misc{reference.wolfram_2025_factorsquarefreelist, author="Wolfram Research", title="{FactorSquareFreeList}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/FactorSquareFreeList.html}", note=[Accessed: 22-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_factorsquarefreelist, organization={Wolfram Research}, title={FactorSquareFreeList}, year={2023}, url={https://reference.wolfram.com/language/ref/FactorSquareFreeList.html}, note=[Accessed: 22-August-2025]}