4MA0 Higher June 2017 Paper 3R Q21

21 Here is a shape \(ABCDE\).

Diagram NOT accurately drawn

\(ABDE\) is a rectangle in which \(AB = 2BD\)
\(BCD\) is a triangle in which angle \(BCD = 120^\circ\)

\(BC = (x - 3)\) cm \(\qquad CD = (x - 2)\) cm

The area of the rectangle \(ABDE\) is \(S\) cm\(^2\)

Show that \(S\) can be expressed in the form \(S = ax^2 + bx + c\)
where \(a\), \(b\) and \(c\) are integers to be found.

(5)