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Gauss's lemma says If the primitive polynomial $f(x)$ can be factored as product of two polynomials having rational coefficients, it can be factored as the product of two polynomials having integer coefficient.

My doubt is why is the condition that $f(x)$ is primitive necessary? Isn't true for all integer polynomials?

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    http://en.wikipedia.org/wiki/Gauss's_lemma_(polynomial)#A_proof_valid_over_any_GCD_domain The irreducibility statement there might help understand, non?2011-11-13
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    Note: "doubt" here is used in the sense of Indian English ... http://meta.math.stackexchange.com/questions/3200/2011-11-13
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    Amazingly, this meaning confirms to my naive concept of this word!! Although I am certainly not an Indian...2011-11-13

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