- (a) Factorise completely \(x ^ { 3 } - 4 x\)
(b) Sketch the curve \(C\) with equation
$$y = x ^ { 3 } - 4 x ,$$
showing the coordinates of the points at which the curve meets the \(x\)-axis.
The point \(A\) with \(x\)-coordinate - 1 and the point \(B\) with \(x\)-coordinate 3 lie on the curve \(C\).
(c) Find an equation of the line which passes through \(A\) and \(B\), giving your answer in the form \(y = m x + c\), where \(m\) and \(c\) are constants.
(d) Show that the length of \(A B\) is \(k \sqrt { } 10\), where \(k\) is a constant to be found.