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Extension
Extension is an option for Factor, PolynomialGCD and related functions which specifies what algebraic numbers to allow in the coefficients of resulting polynomials.
With the setting Extension->
,
, ...  any rational combination of the  can appear.
The  must be exact numbers. They can involve I, n
 roots, and Root objects.
The  can be viewed as generators for the algebraic number field in which the coefficients are assumed to lie.
With the default setting Extension->None all coefficients are required to be rational numbers, and any algebraic numbers that appear in input polynomials are treated like independent variables.
Extension->Automatic includes any algebraic numbers from the input polynomials in the coefficient field.
Extension->
,
, ...  includes both the  and any algebraic numbers from the input polynomials in the coefficient field.
GaussianIntegers->True is equivalent to Extension->I.
See the Mathematica book: Section 3.3.6.
See also: Modulus.
Further Examples
See the Further Examples for Factor, Cancel, Together, PolynomialGCD.
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