2025 ESSS P2 Q6

The function \(\mathrm{f}(x)\) is defined by \(\mathrm{f}(x)=x^3+px^2+qx-12\) for all real \(x\). Given that \(x-3\) is a factor of \(\mathrm{f}(x)\) and that when \(\mathrm{f}(x)\) is divided by \(x+2\) the remainder is \(10\).

1. Find the value of each of the constants \(p\) and \(q\),[4]
2. Express \(\mathrm{f}(x)\) as the product of linear factors.[3]