5 The polynomial $\mathrm { p } ( x )$ is defined by

$$\mathrm { p } ( x ) = 6 x ^ { 3 } + a x ^ { 2 } + b x - 20$$

where $a$ and $b$ are constants. It is given that $( x + 2 )$ is a factor of $\mathrm { p } ( x )$ and that the remainder is - 11 when $\mathrm { p } ( x )$ is divided by $( x + 1 )$.\\
(a) Find the values of $a$ and $b$.\\

(b) Hence factorise $\mathrm { p } ( x )$, and determine the exact roots of the equation $\mathrm { p } ( 3 x ) = 0$.\\

\hfill \mbox{\textit{CAIE P2 2023 Q5}}