2.
$$f ( x ) = 2 x ^ { 3 } + 5 x ^ { 2 } + 2 x + 15$$
- Use the factor theorem to show that \(( x + 3 )\) is a factor of \(\mathrm { f } ( x )\).
- Find the constants \(a\), \(b\) and \(c\) such that
$$f ( x ) = ( x + 3 ) \left( a x ^ { 2 } + b x + c \right)$$
- Hence show that \(\mathrm { f } ( x ) = 0\) has only one real root.
- Write down the real root of the equation \(\mathrm { f } ( x - 5 ) = 0\)