Let f(x) be a polynomial such that f(0) = 4, f(1) = -5, and f(2) = 10. Find the remainder when f(x) is divided by x(x - 1)(x - 2).
Remainder of f(x) R(x) when divided by x(x-1)(x-2) must be polynomial of lower degree than x(x-1)(x-2).
Let R(x) be ax2 + bx + c.
f(0) = 4 => R(0) = 4 = c
f(1) = -5 => R(1) = a + b + c = -5 = a + b = -9
f(2) = 10 => R(2) = 4a + 2b + c = 10 = 4a + 2b = -14
a + b = -9, 4a + 2b = -14
a = 2, b = -11
R(x) = 2x2 - 11x + 4.
