2025 IGCSE Additional Mathematics October/November 0606/21 Q1

The polynomial \(\mathrm p\) is such that \(\mathrm p(x)=x^3+ax^2+bx-2\), where \(a\) and \(b\) are constants.

It is given that:

• \(x+2\) is a factor of \(\mathrm p(x)\)
• when \(\mathrm p(x)\) is divided by \(x-3\) the remainder is 40.

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