The polynomial \(8x^3 + ax^2 + bx - 1\), where \(a\) and \(b\) are constants, is denoted by \(p(x)\). It is given that \((x + 1)\) is a factor of \(p(x)\) and that when \(p(x)\) is divided by \((2x + 1)\) the remainder is 1.

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

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