Polynomials, Cubic Equations and Partial Fractions - Forming Polynomials from Roots and Factors

The cubic polynomial \(\mathrm{f}(x)\) is such that the coefficient of \({{x}^{3}}\) is \(2\) and the roots of the equation \(\mathrm{f}(x)=0\) are \(-1,\mathrm{ }3,\)and \(k\). Given that \(\mathrm{f}(x)\)has a remainder of \(20\) when divided by \(x-4\), show that \(k=2\). Hence or otherwise, find the remainder when \(\mathrm{f}(x)\) is divided by \(2x-1\).