4. \(\mathrm { f } ( x ) = ( x - 3 ) \left( 3 x ^ { 2 } + x + a \right) - 35\) where \(a\) is a constant
- State the remainder when \(\mathrm { f } ( x )\) is divided by \(( x - 3 )\).
Given \(( 3 x - 2 )\) is a factor of \(\mathrm { f } ( x )\),
- show that \(a = - 17\)
- Using algebra and showing each step of your working, fully factorise \(\mathrm { f } ( x )\).