Consider the quartic polynomial s(x)=2x4−9x3−2x2+39x−18.
(i) Show that x=3 is a zero of s(x).
(ii) Divide s(x) by the corresponding linear factor found in part (i) and write the cubic quotient obtained.
(iii) Verify whether x=2 is a zero of the cubic quotient from part (ii). If so, factorise the quotient further.
(iv) Hence, express s(x) as a product of linear factors and state all its zeros.