The volume (in cubic metres) of a rectangular box is modelled by V(x)=x3−9x2+26x−24, where x represents one edge length in metres.
a. (i) Show that V(2)=0.
b. (ii) Obtain the quadratic factor of V(x) after removing the factor corresponding to x=2.
c. (iii) Factorise the quadratic obtained in part (ii).
d. (iv) Hence list all positive integer values of x that make V(x)=0 and interpret each as a possible edge length of the box.