A cubic polynomial is given by s(x)=kx3+2x2−7x+1, where k is a constant.
(i) If the remainder obtained on dividing s(x) by (x−2) is −3, determine the value of k.
(ii) Using the value of k found in part (i), find the remainder when s(x) is divided by (x+1).
(iii) Verify your result in part (ii) by direct substitution of x=−1 in s(x) with the determined value of k.