The FOIL page explains FOIL, which means First, Outer, Inner, Last.
The Polynomial Remainder Theorem says:
If f(x) is a polynomial, then the remainder obtained by dividing f(x) by x-r equals f(r)
In other words, x-r is a factor of f(x)-f(r)
One of the special results of this theorem is this: if the coefficients of a polynomial add up to zero, then the polynomial is divisible by (x-1).
The webmaster and author of this Math Help site is Graeme McRae.