The polynomial \(p(x)\) is defined by \(p(x)=2x^3+ax^2+bx-49\), where \(a\) and \(b\) are constants. When \(p'(x)\) is divided by \(x+3\), the remainder is \(-24\).

(i) Show that \(6a-b=78\).

It is now given that \(2x-1\) is a factor of \(p(x)\).

(ii) Find the values of \(a\) and \(b\).

(iii) Express \(p(x)\) in the form \((2x-1)Q(x)\), where \(Q(x)\) is a quadratic expression.

(iv) Hence factorise \(p(x)\) completely.