BUILT-IN MATHEMATICA SYMBOL

# 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 .

## Details and OptionsDetails and Options

• 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 , 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.

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Factor polynomials:

 Out[1]=
 Out[2]=
 Out[3]=

Factor modulo 2:

 Out[1]=