Final answer:
Rome's decision to send assistance to the Mamertines was driven by economic interests, geopolitical strategy, and maintaining an alliance.
Step-by-step explanation:
The factors that explain Rome's decision to send assistance to the Mamertines consisted of economic interests, geopolitical strategy, and maintaining an alliance. Option 1: Economic interests - The Mamertines controlled the strategic city of Messana, which had a profitable harbor and fertile lands. Rome saw this as an opportunity to gain economic benefits from trade and resources. Option 2: Geopolitical strategy - Rome wanted to expand its influence and control in Sicily, which was a crucial region for trade and maritime power. Assisting the Mamertines would help Rome establish a foothold in the region and counterbalance Carthaginian influence. Option 3: Maintaining an alliance - The Mamertines had previously requested Roman assistance against the Carthaginians. Rome saw this as an opportunity to strengthen an alliance and gain a strategic advantage against its rivals.