The rational root theorem (RRT) says that if you have a polynomial an x^n + ... + a1 x + a0 with integer coefficients, then the only possible rational roots are fractions ±p/q (in simplest form) where p is a factor of a0 (the constant term) and q is a factor of a_n (the leading coefficient). They might not really be roots, but RRT says these are the only POSSIBILITIES.