The polynomial \(\mathrm { f } ( x )\) is defined by \(\mathrm { f } ( x ) = 8 x ^ { 3 } + 6 x ^ { 2 } - 14 x - 1\).
Find the remainder when \(\mathrm { f } ( x )\) is divided by \(( 4 x - 1 )\).
The polynomial \(\mathrm { g } ( x )\) is defined by \(\mathrm { g } ( x ) = 8 x ^ { 3 } + 6 x ^ { 2 } - 14 x + d\).
Given that \(( 4 x - 1 )\) is a factor of \(\mathrm { g } ( x )\), find the value of the constant \(d\).
Given that \(\mathrm { g } ( x ) = ( 4 x - 1 ) \left( a x ^ { 2 } + b x + c \right)\), find the values of the integers \(a , b\) and \(c\).
(3 marks)