2010/040) Let f(x) be a polynomial of degree>2

if f(x) is divided by (x-1) and(x-2)...?
it leaves a remainder 0,2 respectively.what is the remainder when f(x) is divided by (x-1)(x-2).

if f(x) is divided by (x-1)(x-2) remainder shall be a polynomial of degree 1

f(x) = p(x)(x-1)(x-2) + a x +b

f(1) = a + b = 0 so a = - b is the remainder when divided by (x-1)

f(2) = 2a + b = 2 so -2b +b = 2 or b - 2 and a = 2

so remainder = 2x - 2