For a certain model of a container, the net capacity (in cubic centimetres) as a function of the thickness t (in centimetres) of its lining is given by
C(t)=t3−4t2−t+4.
Answer the following.
(i) Verify whether t=1 is a value at which the capacity becomes zero.
(ii) Obtain the other factor(s) of C(t) by dividing by the appropriate linear expression.
(iii) Hence factorise C(t) completely and determine all thickness values for which the capacity of the container is zero.