Polynomials, Cubic Equations and Partial Fractions - Polynomial Division and Remainders

Given that \(4{{x}^{3}}-3{{x}^{2}}-5x+2\equiv \left( Ax+B \right)\left( x-2 \right)\left( x+3 \right)+C\left( x-2 \right)+D\) for all values of \(x\).

1. Find the values of \(A\), \(B\), \(C\), and \(D\).
2. Hence, deduce the remainder when \(4{{x}^{3}}-3{{x}^{2}}-5x+2\) is divided by \({{x}^{2}}+x-6\).