 If formula_90 is a rational root of such a polynomial 
the factor theorem shows that one has a factorization
where both factors have integer coefficients (the fact that has integer coefficients results from the above formula for the quotient of by formula_93).Comparing the coefficients of degree and the constant coefficients in the above equality shows that, if formula_90 is a rational root in reduced form, then is a divisor of formula_95 and is a divisor of formula_96 Therefore, there is a finite number of possibilities for and , which can be systematically examined.For example, if the polynomial 
has a rational root formula_98 with , then must divide 6; that is formula_99 and must divide 2, that is formula_100 Moreover, if , all terms of the polynomial are negative, and, therefore, a root cannot be negative.