This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 Factor Factor[ poly ] factors a polynomial over the integers. Factor[ poly , Modulus-> p ] factors a polynomial modulo a prime p. Factor[ poly , Extension-> , , ... ] factors a polynomial allowing coefficients that are rational combinations of the algebraic numbers . Factor applies only to the top 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. See the Mathematica book: Section 1.4.3, Section 1.4.5, Section 3.3.1. See also Implementation NotesA.9.55.3MainBookLinkOldButtonDataA.9.55.3. See also: FactorTerms, FactorSquareFree, Solve, Expand, Simplify, FactorInteger, TrigFactor. Further Examples We factor a few polynomials over the integers. In[1]:= Out[1]= In[2]:= Out[2]= In[3]:= Out[3]= Some polynomials that don't factor over the integers do factor over the integers modulo a prime. In[4]:= Out[4]= In[5]:= Out[5]= Without specifying the appropriate extension field, you cannot factor either of these polynomials into linear factors. In[6]:= Out[6]= Without specifying the appropriate extension field, you cannot factor either of these polynomials into linear factors. In[7]:= Out[7]= You can factor them into linear terms by specifying the extension. In[8]:= Out[8]= In[9]:= Out[9]= Factor will use multiple-angle formulas for with the setting Trig -> True, and using the option GaussianIntegers may do more factorization. In[10]:= Out[10]= In[11]:= Out[11]= In[12]:= Out[12]= Here we factor a polynomial in three variables with 195 terms. In[13]:= Out[13]=