3 The polynomial \(a x ^ { 3 } + b x ^ { 2 } + x + 3\), where \(a\) and \(b\) are constants, is denoted by \(\mathrm { p } ( x )\). It is given that \(( 3 x + 1 )\) is a factor of \(\mathrm { p } ( x )\), and that when \(\mathrm { p } ( x )\) is divided by \(( x - 2 )\) the remainder is 21 . Find the values of \(a\) and \(b\).
3 The polynomial $a x ^ { 3 } + b x ^ { 2 } + x + 3$, where $a$ and $b$ are constants, is denoted by $\mathrm { p } ( x )$. It is given that $( 3 x + 1 )$ is a factor of $\mathrm { p } ( x )$, and that when $\mathrm { p } ( x )$ is divided by $( x - 2 )$ the remainder is 21 . Find the values of $a$ and $b$.
\hfill \mbox{\textit{CAIE P3 2014 Q3}}