A rectangular box has width (x−4) cm. Its volume, expressed in terms of x, is V(x)=x3−5x2−2x+24 cubic centimetres. The length and height are each linear polynomials in x.
(i) Factorise V(x) completely into three linear factors.
(ii) Hence determine algebraic expressions for the length and height of the box in terms of x.
(iii) Using the factors obtained, calculate the volume of the box when x=6 cm.