If x_0 is a root of polynomial w(x) then a polynomial w(x) can divide by x - x_0. If polynomial w(x) can divide by x - x_0 then x_0 is a root of polynomial w(x). Example: w(x) = x^3+x^2-2, w(1) = 1^3 + 1^2 - 2 = 1+1-2 = 0. Number 1 is a root of polynomial x^3 + x^2 - 2 thus this polynomial cat divide by x - 1 and remainder not exists.