The polynomial \(\mathrm p(x)=ax^3+bx^2+6x+4\), where \(a\) and \(b\) are integers, is divisible by \(x-2\). When \(\mathrm p'(x)\) is divided by \(x+1\), the remainder is \(-7\).

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

(b) Using your answers to part (a), find the remainder when \(\mathrm p''(x)\) is divided by \(x\).