Let q(x)=2x3−5x2+3x−9.
(i) Divide q(x) by (x−3) and write the remainder.
(ii) Using the remainder obtained in part (i), explain what conclusion can be drawn about x=3 in relation to q(x).
(iii) On the basis of your explanation in part (ii), describe the general relationship between the remainder when a polynomial p(x) is divided by (x−a) and the value p(a).