2.5: Unknown coefficient from a factor

0606/22/M/J/16 — Question 4 · 5 marks

Do not use a calculator in this question.

The polynomial p(x)=2x3−3x2+qx+56p(x) = 2x^{3} - 3x^{2} + qx + 56 has a factor x−2x - 2.
(i)
Show that q=−30q = -30.
[1]
(ii)
Factorise p(x)p(x) completely and hence state all the solutions of p(x)=0p(x) = 0.
[4]