Primitive part and content: Difference between revisions

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In [[algebra]], the '''content''' of a [[polynomial]] with integer coefficients is the [[highestgreatest common factor]] of its coefficients. Thus, e.g., the content of <math>12x^3+30x-20</math> equals 2, since this is the greatest common factor of 12, 30, and -20. The definition may be extended to polynomials with coefficients in any fixed [[unique factorization ___domain]].

A polynomial is ''[[Primitive polynomial (ring theory)|primitive]]'' if it has content unity.

[[Gauss's lemma (polynomial)|Gauss's lemma for polynomials]] maystates bethat expressedthe asproduct statingof that forprimitive polynomials over(with acoefficients in the same [[unique factorization ___domain]]) also is primitive. Equivalently, it may be expressed as stating that for the content of the product of two polynomials is the product of their contents.

==See also==