2025 NASS P2 Q7

The diagram shows part of the curve \(y=x^3+3x^2-13x-15\) and the line \(y=9x+9\). The curve intersects the line at the points \(A\), \(B\) and \(C\). The curve intersects the \(x\)-axis at points \((-5,0)\), \((3,0)\) and point \(B\).

1. Find the coordinates of points \(A\) and \(B\).[4]
2. Hence find the area of the shaded region.[6]