Let be an integer polynomial. The can be factored into a product of two polynomials of lower degree with rational coefficients iff it can be factored into a product of integer polynomials of lower degree.
Gauss's Polynomial Theorem
See alsoAbel's Irreducibility Theorem, Abel's Lemma, Gauss's Polynomial Identity, Kronecker's Polynomial Theorem, Polynomial, Schönemann's Theorem
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ReferencesDörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, p. 119, 1965.
Referenced on Wolfram|AlphaGauss's Polynomial Theorem
Cite this as:
Weisstein, Eric W. "Gauss's Polynomial Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GausssPolynomialTheorem.html