10. The curve with equation \(y = ( 2 - x ) ( 3 - x ) ^ { 2 }\) crosses the \(x\)-axis at the point \(A\) and touches the \(x\)-axis at the point \(B\).
- Sketch the curve, showing the coordinates of \(A\) and \(B\).
- Show that the tangent to the curve at \(A\) has the equation
$$x + y = 2$$
Given that the curve is stationary at the points \(B\) and \(C\),
- find the exact coordinates of \(C\).