2025 JVSS PRELIMS P2 Q6

The function \(f(x)=x^3+px^2+qx-12\), where \(p\) and \(q\) are constants, has a factor \(x+1\) and leaves a remainder of 36 when divided by \(x-3\).

1. Show that \(p=5\) and \(q=-8\).[4]
2. Using these values of \(p\) and \(q\), solve the equation \(f(x)=0\).[2]