|If f(x) is a polynomial in x and is divided by x-a 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 (x-a)
By division algorithm,
Dividend = (Quotient x Divisor) + Remainder
p(x) = q(x).(x-a) + R
Substitute x = a
p(a) = q(a).(a-a) + R
p(a) = R(a-a = 0, 0-q(a) = 0)
Hence remainder = p(a)
Example: Find the remainder when 2x3 + 4 is divided by (x-1)
Example: Factorise x2 +3x + 4 using remainder theorem.
Directions: Solve the following.