\(f ( 1 ) = 4, f ( 2 ) = 0\), so \(( x - 2 )\) is a factor. Knowing this factor, we can take a shortcut and divide this factor into \(f ( x )\) to get \(( x^2 - 2 x - 3 )\) which we can factor by conventional means as \(( x - 3 ) ( x + 1 )\). Thus, \(f ( x ) = ( x - 2 ) ( x - 3 ) ( x + 1 )\).
So the zeros are 2, 3 and \(-1\).