The Rational Root Theorem
The rational root theorem states that possible roots for a polynomial can be identified using factors of the constant term (p) and factors of the leading coefficient (q) and take the form of p/q.
For example, suppose the polynomial equation was x2 + 10x + 25 = 0, then p = 25 and q = 1.
Thus factors of p include +/- 1, 5, 25 while factors of q include +/- 1.
The list of all possible rational roots would then be +/- (25/1), (5/1), (1/1).
Using synthetic division, one can quickly determine whether a root is valid.