The polynomial \(p(x)=6x^3+ax^2+6x+b\), where \(a\) and \(b\) are integers, is divisible by \(2x-1\). When \(p(x)\) is divided by \(x-2\), the remainder is \(120\).

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

(b) Hence write down the remainder when \(p(x)\) is divided by \(x\).

(c) Find the value of \(p''(0)\).