Polynomial Question

Question

When the polynomial P(x) is divided by x-1, the remainder is 2, and when divided by x-2 the remainder is 1. What is the remainder when P(x) is divided by (x-1)(x-2).

Answer 1

What we know is that the polynomial passes through the points (1,2) and (2,1). This is from the theorem which states that the remainder, when a polynomial P(x) is divided by x-a, is P(a)

The straight line through those two points is such a polynomial.

y=-x+3