The polynomial \(p(x)\) is \(ax^3+bx^2-13x+4\), where \(a\) and \(b\) are integers. Given that \(2x-1\) is a factor of \(p(x)\) and also a factor of \(p'(x)\),

(i) find the value of \(a\) and of \(b\).

Using your values of \(a\) and \(b\),

(ii) find the remainder when \(p(x)\) is divided by \(x+1\).