find the values of P, q and r such that when the polynomial f(x) = x^3 + Px^2 +qx + r is divided by (x+2), (x-1) and (x-3), the reminders are respectively, -48, 0 and 2

Hint: Use remainder theorem.

f(-2) = -8+4p-2q+r = -48

f(1) = 1+p+q+r = 0

f(3) = 27+9p+3q+r = 2

Solving the system gives you the answer.