Gauss' Lemma

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Gauss' Lemma

If [math]f(x)[/math] is a polynomial with integer coefficients with deg [math]f(x) \geq 1[/math]. Then [math] f(x)[/math] is irreducible over [math] \Q \iff [/math] when [math] f(x) = g(x)h(x) [/math] with [math] g(x), h(x) \in \Z [x] [/math], then deg [math]g(x) = 0[/math] or deg [math]h(x) = 0 [/math].