Consider the polynomial
p(x)=2x3−5x2−14x+8.
(i) Show that x=4 is a zero of p(x).
(ii) Divide p(x) by (x−4) and write down the resulting quadratic quotient.
(iii) Factorise the quadratic quotient obtained in part (ii) completely and hence express p(x) as a product of its linear factors.
(iv) List all the real zeros of p(x).