Do not use a calculator in this question.

(a) Show that \(x+3\) is a factor of

\(-12+23x+3x^2-2x^3.\)

(b) The curve

\(y=-5+33x+3x^2-2x^3\)

and the line

\(y=10x+7\)

intersect at three points, \(A\), \(B\) and \(C\). These points are such that the \(x\)-coordinate of \(A\) has the least value and the \(x\)-coordinate of \(C\) has the greatest value. Show that \(B\) is the midpoint of \(AC\).