The polynomial \(x^3 - 2x + a\), where \(a\) is a constant, is denoted by \(p(x)\). It is given that \((x + 2)\) is a factor of \(p(x)\).

(i) Find the value of \(a\).

(ii) When \(a\) has this value, find the quadratic factor of \(p(x)\).