2. \(\mathrm { f } ( x ) = x ^ { 3 } + a x ^ { 2 } + b x - 10\), where \(a\) and \(b\) are constants. When \(\mathrm { f } ( x )\) is divided by \(( x - 3 )\), the remainder is 14 . When \(\mathrm { f } ( x )\) is divided by \(( x + 1 )\), the remainder is - 18 .

1. Find the value of \(a\) and the value of \(b\).
2. Show that \(( x - 2 )\) is a factor of \(\mathrm { f } ( x )\).
   [0pt] [P3 June 2002 Question 1]