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

Determine the values of \(p\) and \(q\) for which the polynomial \(\mathrm{f}\left( x \right)={{x}^{4}}+p{{x}^{2}}+qx+8\) is divisible by \({{x}^{2}}+3x+2\).