 If it has a rational root, its denominator must divide evenly.So, it may be written as a possibly reducible fraction formula_105 By Vieta's formulas, the other root is
with formula_107
Thus the second root is also rational, and the second Vieta's formula gives
that is 
Checking all pairs of integers whose product is gives the rational roots, if any.For example, let consider the quadratic polynomial
Inspection of the factors of leads to , giving the two roots 

and the factorization 

Any univariate quadratic polynomial formula_113 can be factored using the quadratic formula