Question

A polynomial p (x) when divided by x-1 gives remainder 1, when divided by x-2 gives remainder 2. What will be the remainder when p (x) is divided by (x-1)(x-2)

Answer 1

By remainder theorem we have

p(1) = 1 , and , p(2) = 2

Let p(x) = (x-1)(x-2)*g(x) + ax + b , where g(x) is a polynomial not equal to 0

For x = 1 , p(1) = a(1) + b or 1 = a+b

For x = 2, p(2) = a(2) + b or 2 = 2a+b

Solving these two equations we have a = 1 and b = 0

Thus remainder is x