The volume (in cubic centimetres) of a rectangular box is given by
V(x)=x3−9x2+26x−24,
where x centimetres represents one edge of the box.
a. (i) Show that x=2 makes the volume zero and state the corresponding linear factor of V(x).
b. (ii) Factorise V(x) completely.
c. (iii) Find all integral values of x for which the volume becomes zero.
d. (iv) Which of the values obtained in part (iii) can represent the actual edge length of the box? Give a reason for your answer.