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# 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 .
• 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.
• 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 automatically threads over lists, as well as equations, inequalities and logic functions.
Factor polynomials:
Factor modulo 2:
Factor polynomials:
 Out[1]=
 Out[2]=
 Out[3]=

Factor modulo 2:
 Out[1]=
 Scope   (3)
A univariate polynomial:
A multivariate polynomial:
A rational function:
Some non-polynomial expressions can be factored:
 Options   (5)
Factor over algebraic number fields:
Extension automatically extends to a field that covers the coefficients:
Factor over Gaussian integers:
Factor over finite fields:
Factor a trigonometric expression:
Expand is effectively the inverse of Factor:
FactorList gives a list of factors:
FactorSquareFree only pulls out multiple factors:
The first factoring of where a appears as a coefficient:
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