The polynomial \(p(x)=ax^3+bx^2+cx-9\) is divisible by \(x+3\). It is given that \(p'(0)=36\) and \(p''(0)=86\).

(i) Find the value of each of the constants \(a\), \(b\) and \(c\).

(ii) Using your values of \(a\), \(b\) and \(c\), find the remainder when \(p(x)\) is divided by \(2x-1\).