 Then one divides out the greater common divisor of the coefficients of this polynomial for getting the primitive part, the content being formula_81 Finally, if needed, one changes the signs of and all coefficients of the primitive part.This factorization may produce a result that is larger than the original polynomial (typically when there are many coprime denominators), but, even when this is the case, the primitive part is generally easier to manipulate for further factorization.The factor theorem states that, if is a root of a polynomial
(that is ), then there is a factorization 
where 
with formula_85 and
for .