2023 KSS P2 Q7

The diagram shows the line \(y=x+12\) intersecting the curve \(y=x^3-3x^2-3x+12\) at the point \(A\) and intersecting the line \(x=2\) at the point \(B\). The line \(x=2\) also intersects the curve at the point \(C\). Find

1. the coordinates of \(A\) and of \(B\).[5]
2. the area of the shaded region \(ABC\).[6]