A consequence of the remainder theorem, the factor theorem states:

Let f(x) be a polynomial. Then x−h is a factor of f(x) if and only if f(h)=0.

The theorem is helpful investigating factorization over the integers. For example, to factorize f(x) = 6x³ + 19x² + 16x + 4, if x−h is a factor, where h is an integer, then h must divide 4. We may note f(−2)=−48 + 76−32 + 4=0, and so x + 2 is a factor. To appreciate that 2x + 1 is a factor, we need to calculate f(−1/2).