6 The cubic polynomial \(\mathrm { p } ( x )\) is given by \(\mathrm { p } ( x ) = ( x - 2 ) \left( x ^ { 2 } + x + 3 \right)\).
- Show that \(\mathrm { p } ( x )\) can be written in the form \(x ^ { 3 } + a x ^ { 2 } + b x - 6\), where \(a\) and \(b\) are constants whose values are to be found.
- Use the Remainder Theorem to find the remainder when \(\mathrm { p } ( x )\) is divided by \(x + 1\).
(2 marks) - Prove that the equation \(( x - 2 ) \left( x ^ { 2 } + x + 3 \right) = 0\) has only one real root and state its value.
(3 marks)