I want to know the most probable meaning of "exterminare" in this passage from canon 3 of the Lateran IV Ecumenical Council of 1215  , specifically whether it is "kill" or "expel":
ita pro defensione fidei praestent publice iuramentum quod de terris suae iurisdictioni subiectis universos haereticos ab ecclesia denotatos bona fide pro viribus exterminare studebunt
Whereas the passage is usually translated as in :
so for the defense of the faith they ought publicly to take an oath that they will strive in good faith and to the best of their ability to exterminate in the territories subject to their jurisdiction all heretics pointed out by the Church
... a few Catholic sites have translated "de terris suae iurisdictioni subiectis [...] exterminare" as "to expel from the lands subject to their jurisdiction".
To the extent that actions may provide context for translation, heretics after 1215 were everywhere burned, not expelled. The foremost case was that of Jan Hus, who was condemned to death and burned in 1415 in the presence of the assembly of all the bishops attending the ecumenical council of Constance. If the Lateran IV Council had ordered to expel heretics, not to kill them, how didn't a single bishop come up and say "Wait, exterminare in Lateran IV means expel, not kill!"?
Additionally, does "pro viribus" before "exterminare" mean "manly"? If that's the case, it fits exterminare = kill more than exterminare = expel.
 Lateran IV, English & Latin: http://ldysinger.stjohnsem.edu/@magist/1215_Lateran4_ec12/02_lat4_c01-22.htm
 Lateran IV, Latin only: http://www.documentacatholicaomnia.eu/03d/1215-1215,_Concilium_Lateranense_IIII,_Documenta,_LT.pdf