2 In this question you must show detailed reasoning.
The equation \(\mathrm { f } ( x ) = 0\), where \(\mathrm { f } ( x ) = x ^ { 4 } + 2 x ^ { 3 } + 2 x ^ { 2 } + 26 x + 169\), has a root \(x = 2 + 3 \mathrm { i }\).
- Express \(\mathrm { f } ( x )\) as a product of two quadratic factors.
- Hence write down all the roots of the equation \(\mathrm { f } ( x ) = 0\).