1.
$$f ( x ) = p x ^ { 3 } + 6 x ^ { 2 } + 12 x + q .$$
Given that the remainder when \(\mathrm { f } ( x )\) is divided by ( \(x - 1\) ) is equal to the remainder when \(\mathrm { f } ( x )\) is divided by ( \(2 x + 1\) ),
- find the value of \(p\).
Given also that \(q = 3\), and \(p\) has the value found in part (a),
- find the value of the remainder.