2025 PHS P2 Q3

The polynomial \(\mathrm{f}(x)=x^3+ax^2+bx+70\) for all real \(x\). Given that \(x-2\) is a factor of \(\mathrm{f}(x)\) and that when \(\mathrm{f}(x)\) is divided by \(x-3\) the remainder is \(-32\).

1. Find the value of each of the constants \(a\) and \(b\).[4]
2. Hence, solve \(\mathrm{f}(x)=0\).[3]