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[poly,Modulus->p] factors modulo a prime p.
  • FactorList[poly,GaussianIntegers->True] allows Gaussian integer coefficients.
  • FactorList[poly,Extension->{a1,a2,}] allows coefficients that are arbitrary rational combinations of the ai.


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Basic Examples  (1)

List factors of polynomials:

Scope  (4)

A univariate polynomial:

A multivariate polynomial:

A polynomial with multiple factors:

A rational function:

Options  (5)

Extension  (2)

Factor over algebraic number fields:

Extension->Automatic automatically extends to a field that covers the coefficients:

GaussianIntegers  (1)

Factor over Gaussian integers:

Modulus  (1)

Factor over finite fields:

Trig  (1)

Factor a trigonometric expression:

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:

Introduced in 1988
Updated in 1996