6 The polynomial \(\mathrm { p } ( x )\) is defined by
$$\mathrm { p } ( x ) = x ^ { 3 } + 2 x + a$$
where \(a\) is a constant.
- Given that \(( x + 2 )\) is a factor of \(\mathrm { p } ( x )\), find the value of \(a\).
- When \(a\) has this value, find the quotient when \(\mathrm { p } ( x )\) is divided by ( \(x + 2\) ) and hence show that the equation \(\mathrm { p } ( x ) = 0\) has exactly one real root.