This video shows how to prove that if (x-a) is a factor of the function f(x), that is if (x-a) divides into f(x) exactly with no remainder, then the value of the function at point a, f(a) is zero. This is an example of algebraic proof.
Remainder theorem that if a polynomial which maybe represented by f(x) has a factor of (x-k), then the remainder is f(k)=0. If a factor is (ax-b),then the remainder is f(b/a)=0.(as ax-b=0 ,x= b/a)