FactorList

FactorList[poly]
gives a list of the factors of a polynomial, together with their exponents.

The first element of the list is always the overall numerical factor. It is if there is no overall numerical factor.

FactorList[poly, Extension->{a₁, a₂, ...}] allows coefficients that are arbitrary rational combinations of the .

List factors of polynomials:

Out[1]=

Out[2]=

A univariate polynomial:

A multivariate polynomial:

A polynomial with multiple factors:

A rational function:

Factor over algebraic number fields:

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

Factor over Gaussian integers:

Factor over finite fields:

Factor a trigonometric expression:

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: