THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.

DOCUMENTATION CENTER SEARCH

New to Mathematica? Find your learning path »

Mathematica > Mathematics and Algorithms > Formula Manipulation > Algebraic Transformations > Factor >

BUILT-IN MATHEMATICA SYMBOL

Tutorials »|See Also »|More About »

Factor

Factor[poly]
factors a polynomial over the integers.

Factor[poly, Modulus->p]
factors a polynomial modulo a prime p.

Factor[poly, Extension->{a₁, a₂, ...}]
factors a polynomial allowing coefficients that are rational combinations of the algebraic numbers

MORE INFORMATION

Factor applies only to the top algebraic level in an expression. You may have to use Map, or apply Factor again, to reach other levels.

Factor[poly, GaussianIntegers->True] factors allowing Gaussian integer coefficients.

If any coefficients in poly are complex numbers, factoring is done allowing Gaussian integer coefficients.

The exponents of variables need not be positive integers. Factor can deal with exponents that are linear combinations of symbolic expressions.

When given a rational expression, Factor effectively first calls Together, then factors numerator and denominator.

With the default setting Extension->None, Factor[poly] will treat algebraic number coefficients in poly like independent variables.

Factor[poly, Extension->Automatic] will extend the domain of coefficients to include any algebraic numbers that appear in poly. »

Factor automatically threads over lists, as well as equations, inequalities and logic functions.

EXAMPLES

CLOSE ALL

Basic Examples (2)

Factor polynomials:

Factor modulo 2:

Factor polynomials:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

In[3]:=

Out[3]=

Factor modulo 2:

In[1]:=

Out[1]=

Scope (3)

A univariate polynomial:

A multivariate polynomial:

A rational function:

Generalizations & Extensions (1)

Some non-polynomial expressions can be factored:

Options (5)

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:

Properties & Relations (3)

Expand is effectively the inverse of Factor:

FactorList gives a list of factors:

FactorSquareFree only pulls out multiple factors:

Neat Examples (2)

The first factoring of

where a

appears as a coefficient: