2026 NASS P2 Q3

A cubic polynomial is given as \(\mathrm{P}(x)=x^3+ax^2+bx+c\). The graph of \(y=\mathrm{P}(x)\) cuts the \(y\)-axis at \((0,2)\). The remainder when \(\mathrm{P}(x)\) is divided by \(x+1\) is \(-3\), and \(x-2\) is a factor of \(\mathrm{P}(x)\).

1. Find the values of \(a\), \(b\) and \(c\).[4]
2. Hence solve the equation \(\mathrm{P}(x)=0\), leaving your answers in exact form.[3]