# 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[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.

# Examples

open allclose all

## 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:

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
(1.0)
|
Updated in 1996
(3.0)