- (a) Factorise completely \(x ^ { 3 } + 10 x ^ { 2 } + 25 x\)
(b) Sketch the curve with equation
$$y = x ^ { 3 } + 10 x ^ { 2 } + 25 x$$
showing the coordinates of the points at which the curve cuts or touches the \(x\)-axis.
The point with coordinates \(( - 3,0 )\) lies on the curve with equation
$$y = ( x + a ) ^ { 3 } + 10 ( x + a ) ^ { 2 } + 25 ( x + a )$$
where \(a\) is a constant.
(c) Find the two possible values of \(a\).