Using the rational root theorem, we have 8 total possibilities for roots: ±1, ±2, ±3, and ±6. for x = 1, 2 and 3 p(x) = 0, and the remainder theorem states that if and only if p(x) = 0 then x-c is a factor of p(x). this results in p(x) = (x - 1)(x - 2)(x - 3).