4 The polynomial $a x ^ { 3 } - 5 x ^ { 2 } + b x + 9$, where $a$ and $b$ are constants, is denoted by $\mathrm { p } ( x )$. It is given that $( 2 x + 3 )$ is a factor of $\mathrm { p } ( x )$, and that when $\mathrm { p } ( x )$ is divided by $( x + 1 )$ the remainder is 8 .\\
(i) Find the values of $a$ and $b$.\\
(ii) When $a$ and $b$ have these values, factorise $\mathrm { p } ( x )$ completely.

\hfill \mbox{\textit{CAIE P2 2013 Q4}}