2025 Paradigm Sec 3 Mock EOY Q9

[Polynomial]

The function \(\mathrm{f}(x)=x^3-a^2x+b^2\), where \(a\) and \(b\) are positive constants, leaves a remainder of \(1\) when divided by \(x+3\). The function \(\mathrm{g}(x)=3ax^3-2x^2+bx-6\) is exactly divisible by \(x-1\).

1. Find the values of \(a\) and \(b\).[5]