2023 YTSS P1 Q4

The function \(\mathrm f(x)\) is defined by \(\mathrm f(x)=3x^3+hx^2+kx-4\) for all real \(x\). Given that \(3x-1\) is a factor of \(\mathrm f(x)\) and that when \(\mathrm f(x)\) is divided by \(x+1\), the remainder is \(-4\), find the value of each of the constants \(h\) and \(k\).[5]