6 The polynomial \(x ^ { 3 } - 4 x ^ { 2 } + 10 x - 21\) is denoted by \(\mathrm { f } ( x )\).
- Use the factor theorem to show that \(( x - 3 )\) is a factor of \(\mathrm { f } ( x )\).
- The polynomial \(\mathrm { f } ( x )\) can be written as \(( \mathrm { x } - 3 ) \left( \mathrm { x } ^ { 2 } + \mathrm { bx } + \mathrm { c } \right)\) where \(b\) and \(c\) are constants. Find the values of \(b\) and \(c\).
- Show that \(x = 3\) is the only real root of the equation \(\mathrm { f } ( x ) = 0\).