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 also

Abel's Irreducibility Theorem, Abel's Lemma, Gauss's Polynomial Identity, Kronecker's Polynomial Theorem, Polynomial, Schönemann's Theorem## Explore with Wolfram|Alpha

## References

Dörrie, H.*100 Great Problems of Elementary Mathematics: Their History and Solutions.*New York: Dover, p. 119, 1965.

## Referenced on Wolfram|Alpha

Gauss'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