w³-29=(w-∛29)(w²+w∛29+(∛29)²) based on w³-a³=(w-a)(w²+aw+a²) where a=∛29. (∛29)² can be written 29^⅔.
Further factorisation is possible but this involves complex numbers:
w²+aw+a²/4-a²/4+a²=(w+½a)²+3a²/4=(w+½a+½ai√3)(w+½a-½ai√3).
w³-29=(w-∛29)(w+½∛29+½i∛29√3)(w+½∛29-½i∛29√3).