Final answer:
The Republican Party, also known as the Democratic-Republicans, faced internal divisions during the tenures of Madison and Jefferson concerning economic and populist policies.
Step-by-step explanation:
The question asks which statement is true regarding the Republican Party under Madison and Jefferson. The correct answer is that the party faced internal divisions. While in power, the Republican Party, also known as the Democratic-Republicans, underwent internal strife concerning issues such as tariffs on imported goods, government funding for internal improvements, and populist issues aimed at helping the 'common man,' which included reducing or eliminating property requirements for voting.
Despite these challenges, during the presidencies of Thomas Jefferson and James Madison, the Republican Party did not dissolve, nor did it unite with the Federalist Party. Instead, it grew stronger in influence as it continued to shape the policies and the direction of the United States, particularly in the face of the Napoleonic Wars and the subsequent War of 1812.