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In algebra, the rational root theorem (or rational root test, rational zero theorem or rational zero test) states a constraint on rational solutions (or roots) of a polynomialequation

with integer coefficients.

If a0 and an are nonzero, then each rational solution x, when written as a fraction x = p/q in lowest terms (i.e., the greatest common divisor of p and q is 1), satisfies

The rational root theorem is a special case (for a single linear factor) of Gauss's lemmaon the factorization of polynomials. The integral root theorem is a special case of the rational root theorem if the leading coefficient an = 1.

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