A rectangular sheet of metal is being rolled into a tube. The external surface area S(t) (in square centimetres) after t complete turns of rolling is given by
S(t)=2π(3t2−5t+4).
Answer the following questions.
a. (i) Show that S(t) is a polynomial in t and write its degree.
b. (ii) Calculate the surface area after t=2 complete turns.
c. (iii) If one more turn is added, write the new surface-area expression S(t+1) and state whether it is still a polynomial. Give reasons.