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==Properties==
In the remaining of this article, we consider polynomials over a [[unique factorization ___domain]] {{math|''R''}}, which can typically be the ring of [[integer]]s, or a [[polynomial ring]] over a [[field (mathematics)|field]]. In {{math|''R''}}, [[greatest common divisor]]s are well defined, and are unique [[up to]] the multiplication by a [[unit (ring theory)|unit]] of {{math|''R''}}.
The '''content''' {{math|''c''(''P'')}} of a polynomial {{math|''P''}} with coefficients in {{math|''R''}} is the greatest common divisor of its coefficients, and, as such, is defined up to the multiplication by a unit. The '''primitive part''' {{math|pp(''P'')}} of {{math|''P''}} is the quotient {{math|''P''/''c''(''P'')}} of {{math|''P''}} by its content; it is a polynomial with coefficients in {{math|''R''}}, which is unique up to the multiplication by a unit. If the content is changed by multiplication by a unit {{math|''u''}}, then the primitive part must be changed by dividing it by the same unit, in order to keep the equality
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