
If f(x) is a polynomial in x and is divided by xa and if the remainder is the value of f(x) at x = a i,e remainder = f(a). Proof: Let p(x) be a polynomial divided by (xa) By division algorithm, Dividend = (Quotient x Divisor) + Remainder p(x) = q(x).(xa) + R Substitute x = a p(a) = q(a).(aa) + R p(a) = R(aa = 0, 0q(a) = 0) Hence remainder = p(a)
Example: Find the remainder when 2x^{3} + 4 is divided by (x1)
Example: Factorise x^{2} +3x + 4 using remainder theorem.
Directions: Solve the following. 