FactorList [poly]
gives a list of the factors of a polynomial, together with their exponents.
FactorList
FactorList [poly]
gives a list of the factors of a polynomial, together with their exponents.
Details and Options
- The first element of the list is always the overall numerical factor. It is {1,1} if there is no overall numerical factor.
- FactorList takes the following options:
-
- FactorList [poly,Modulus->p] requires that p be prime.
- FactorList [poly,Extension->{a1,a2,…}] allows coefficients that are arbitrary rational combinations of the ai.
Examples
open all close allBasic Examples (2)
List the irreducible factors of polynomials:
List the irreducible factors of multivariate polynomials:
Scope (11)
Basic Uses (4)
A univariate polynomial:
A multivariate polynomial:
A polynomial with multiple factors:
A rational function:
Advanced Uses (7)
The irreducible factors over the Gaussian integers:
The irreducible factors over an algebraic extension:
The irreducible factors over the integers modulo 2:
The irreducible factors over a finite field:
The irreducible factors over an extension of a finite field:
A polynomial irreducible over factors after embedding in a larger field :
List factors of non-polynomial expressions:
List factors of a polynomial of degree :
Options (7)
Extension (4)
Factor over algebraic number fields:
Extension->Automatic automatically extends to a field that covers the coefficients:
Factor a polynomial with integer coefficients over a finite field:
Factor a polynomial with coefficients in a finite field:
Embedding in a larger field allows further factorization:
GaussianIntegers (1)
Factor over Gaussian integers:
Modulus (1)
Factor over finite fields:
Trig (1)
Factor a trigonometric expression:
Applications (2)
FactorList can be useful in determining the behavior of functions:
has roots at and , at it does not cross the axis, and at it crosses the axis:
Show that a polynomial is a perfect square:
Compute the factors and note that the constant factor is positive:
Extract the exponents of nonconstant factors:
Check that every factor has even exponent and thus is a square:
Properties & Relations (3)
FactorList gives a list of irreducible factors:
This multiplies the factors together:
Factor gives a product of factors:
Expand combines all the factors back together:
FactorSquareFreeList gives a list of square-free factors:
FactorInteger gives a list of prime factors of an integer:
Tech Notes
Related Guides
History
Introduced in 1988 (1.0) | Updated in 1996 (3.0) ▪ 2022 (13.2) ▪ 2023 (13.3)
Text
Wolfram Research (1988), FactorList, Wolfram Language function, https://reference.wolfram.com/language/ref/FactorList.html (updated 2023).
CMS
Wolfram Language. 1988. "FactorList." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/FactorList.html.
APA
Wolfram Language. (1988). FactorList. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FactorList.html
BibTeX
@misc{reference.wolfram_2025_factorlist, author="Wolfram Research", title="{FactorList}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/FactorList.html}", note=[Accessed: 16-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_factorlist, organization={Wolfram Research}, title={FactorList}, year={2023}, url={https://reference.wolfram.com/language/ref/FactorList.html}, note=[Accessed: 16-November-2025]}