A solid metal rod shrinks on cooling. Its change in length, in millimetres, relative to a reference temperature is modelled by the polynomial s(x)=x3−9x2+26x−24, where x is the temperature difference in degrees Celsius.
a. (i) Calculate s(2).
b. (ii) What does your answer in part (i) imply about the linear polynomial (x−2) with respect to s(x)?
c. (iii) Factorise s(x) completely.
d. (iv) For what temperature differences x does the model predict no change in length (that is, s(x)=0)?