When the polynomial \(f(x)\) is divided by \((x-3)\) the remainder is 15. When \(f(x)\) is divided by \((x-1)^2\) the remainder is \(2x+1.\) Find the remainder when \(f(x)\) is divided by \((x-3)(x-1)^2 .\)
Thanks in advance.
The remainder is 6x^2 - 3x + 1.