For the single variable case there is an algorithm: http://en.wikipedia.org/wiki/Rational_root_theorem http://en.wikipedia.org/wiki/Rational_root_theorem Wheth

For the single variable case there is an algorithm: http://en.wikipedia.org/wiki/Rational_root_theorem http://en.wikipedia.org/wiki/Rational_root_theorem Whether it is a fast algorithm depends heavily on the sizes of the first and last coefficients, as you have to factorize them.