Polynomials, Cubic Equations and Partial Fractions - Remainder and Factor Theorems

The cubic polynomial \(\mathrm{h}\left( x \right)\) is such that the coefficient of \({{x}^{3}}\) is \(4\) and the roots of the equation \(\mathrm{h}\left( x \right)=0\) are \(-2\), \(5\), and \(k\). Given that \(\mathrm{h}\left( x \right)\) has a remainder of \(-48\) when divided by \(x-2\), show that \(k=1\) and find the remainder when \(\mathrm{h}\left( x \right)\) is divided by \(4x+20\).