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

The term containing the highest power of \(x\) in the polynomial \(\mathrm{g}\left( x \right)\) is \(4{{x}^{3}}\).

The roots of the equation \(\mathrm{g}\left( x \right)=0\) are \(-3\), \(1\), and \(q\).

Find

1. an expression, in terms of \(x\) and \(q\), for \(\mathrm{g}\left( x \right)\) in descending powers of \(x\),
2. the value of \(q\) for which the division of \(\mathrm{g}\left( x \right)\) by \(x+2\) gives a remainder of \(-24\),
3. the remainder when \(\mathrm{g}\left( x \right)\) is divided by \(3x-1\).