3.
$$f ( x ) = 24 x ^ { 3 } + A x ^ { 2 } - 3 x + B$$
where \(A\) and \(B\) are constants.
When \(\mathrm { f } ( x )\) is divided by \(( 2 x - 1 )\) the remainder is 30
- Show that \(A + 4 B = 114\)
Given also that ( \(x + 1\) ) is a factor of \(\mathrm { f } ( x )\),
- find another equation in \(A\) and \(B\).
- Find the value of \(A\) and the value of \(B\).
- Hence find a quadratic factor of \(\mathrm { f } ( x )\).