Solve inequality involving polynomial

2 The polynomial \(2 x ^ { 3 } - x ^ { 2 } + a\), where \(a\) is a constant, is denoted by \(\mathrm { p } ( x )\). It is given that ( \(2 x + 3\) ) is a factor of \(\mathrm { p } ( x )\).

1. Find the value of \(a\).
2. When \(a\) has this value, solve the inequality \(\mathrm { p } ( x ) < 0\).

11 The function f is defined by $$f ( x ) = 4 x ^ { 3 } - 8 x ^ { 2 } - 51 x - 45 \quad ( x \in \mathbb { R } )$$ 11

1. 1. Fully factorise \(\mathrm { f } ( x )\)
      11
2. (ii) Hence, solve the inequality \(\mathrm { f } ( x ) < 0\)
   11
3. The graph of \(y = \mathrm { f } ( x )\) is translated by the vector \(\left[ \begin{array} { l } 7
   0 \end{array} \right]\)
   The new graph is then reflected in the \(x\)-axis, to give the graph of \(y = \mathrm { g } ( x )\)
   Solve the inequality \(\mathrm { g } ( x ) \leq 0\)