The following result about polynomials:
If a polynomial f(x) is divided by x−h, then the remainder is equal to f(h).
It is proved as follows. Divide the polynomial f(x) by x−h to get a quotient q(x) and a remainder which will be a constant, r. This means that f(x)=(x−h)q(x)+r. Replacing x by h in this equation gives r=f(h), thus proving the theorem. An important consequence of the Remainder Theorem is the Factor Theorem.