6 The cubic polynomial \(\mathrm { f } ( x )\) is defined by
$$\mathrm { f } ( x ) = x ^ { 3 } + a x ^ { 2 } + 14 x + a + 1$$
where \(a\) is a constant. It is given that ( \(x + 2\) ) is a factor of \(\mathrm { f } ( x )\).
- Use the factor theorem to find the value of \(a\) and hence factorise \(\mathrm { f } ( x )\) completely.
- Hence, without using a calculator, solve the equation \(\mathrm { f } ( 2 x ) = 3 \mathrm { f } ( x )\).