Consider the polynomial p(x)=2x3−3x2+4x−5.
(i) Divide p(x) by x−2 and write down the quotient and the remainder.
(ii) Without performing division, evaluate p(2).
(iii) Compare your answers from parts (i) and (ii). Explain what this tells you about the relationship between the remainder obtained on dividing a polynomial by x−2 and the value of the polynomial at x=2. State the general principle illustrated by this comparison in your own words.