Final answer:
The Plebeian uprising is the option that is NOT one of the new military methods used by Rome to conquer all of Italy and achieve political unification of the peninsula.
Step-by-step explanation:
The answer to the question is Plebeian uprising. The new military methods that allowed Rome to conquer all of Italy and achieve the first political unification of the peninsula included the use of the javelin, cavalry, and organized infantry. The Plebeian uprising, on the other hand, was a significant event in Roman history that led to social and political changes, but it was not a military method used by Rome to achieve its conquests.
Learn more about Rome's military methods in conquering Italy