The polynomial \(ax^3 + bx^2 + 5x - 2\), where \(a\) and \(b\) are constants, is denoted by \(p(x)\). It is given that \((2x - 1)\) is a factor of \(p(x)\) and that when \(p(x)\) is divided by \((x - 2)\) the remainder is 12.

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

(ii) When \(a\) and \(b\) have these values, find the quadratic factor of \(p(x)\).