Extermination
late Middle English (in the sense ‘drive out’): from Latin exterminat- ‘driven out’, from the verb exterminare, from ex- ‘out’ + terminus ‘boundary’. The sense ‘destroy’ (mid 16th century) comes from the Latin of the Vulgate.
wiktionary
Borrowed from Middle French extermination, itself a learned borrowing from Ecclesiastical Latin exterminātiō.
etymonline
extermination (n.)
mid-15c., exterminacioun, "repulsion;" 1540s, "utter destruction, eradication," from Latin exterminationem (nominative exterminatio) "ejection, banishment," noun of action from past-participle stem of exterminare "drive out, expel, put aside, drive beyond boundaries," also, in Late Latin "destroy," from phrase ex termine "beyond the boundary," from ex "out of" (see ex-) + termine, ablative of termen "boundary, limit, end" (see terminus).
