The polynomial p(x)=x3−4x+1 is to be examined at several points.
(i) Calculate p(−2),p(−1),p(0),p(1) and p(2).
(ii) Arrange these five values in ascending order.
(iii) From your results in part (i), state between which two consecutive integers (if any) the polynomial must have at least one real zero and give a brief reason for your answer.