1. \(\mathrm { f } ( x ) = x ^ { 3 } + a x ^ { 2 } + b x - 10\), 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 \(\mathrm { f } ( x )\).