The polynomial \(ax^3 - 10x^2 + bx + 8\), where \(a\) and \(b\) are constants, is denoted by \(p(x)\). It is given that \((x-2)\) is a factor of both \(p(x)\) and \(p'(x)\).

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

(b) When \(a\) and \(b\) have these values, factorise \(p(x)\) completely.