
Statement: If p(x) is a ploynomial in x, divided by xa and the remainder = f(a) is zero, then (xa) is a factor of p(x). Proof: When p(x) is divided by (xa) R = p(a) (by remainder theorem) p(x) = (xa) q(x) + p(a) From remainder theorem we have (xa) is a factor of p(a) Conversely if xa is a factor of p(x) then p(a) = 0 p(x) = (xa) q(x) + R 