1 The polynomial \(\mathrm { p } ( x )\) is defined by $$\mathrm { p } ( x ) = 4 x ^ { 3 } + ( k + 1 ) x ^ { 2 } - m x + 3 k$$ where \(k\) and \(m\) are constants. Given that \(( x + 1 )\) is a factor of \(\mathrm { p } ( x )\), express \(m\) in terms of \(k\).