Do not use a calculator in this question.

It is given that \(x+4\) is a factor of

\(p(x)=2x^3+3x^2+ax-12.\)

When \(p(x)\) is divided by \(x-1\), the remainder is \(b\).

(i) Show that \(a=-23\) and find the value of the constant \(b\).

(ii) Factorise \(p(x)\) completely and hence state all the solutions of \(p(x)=0\).