The polynomial \(\mathrm{p}\) is such that \(\mathrm{p}(x)=ax^3+11x^2+bx+c\), where \(a\), \(b\) and \(c\) are integers. It is given that \(\mathrm{p}'(0)=12\). It is also given that \(x+3\) is a factor of \(\mathrm{p}\). When \(\mathrm{p}\) is divided by \(x-1\) the remainder is \(16\).
Find the values of \(a\), \(b\) and \(c\).[6]
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