Final answer:
Jefferson's victory in the 1800 election was influenced by the declining support for the incumbent Adams, the strategic interventions by Alexander Hamilton, and the crucial role of the House of Representatives electing Jefferson after a tie in the Electoral College.
Step-by-step explanation:
Factors that led to Thomas Jefferson's victory in the election of 1800 include John Adams' alienation from both Federalists and Republicans, the influential opposition of Alexander Hamilton, and the significant role of the House of Representatives in ultimately deciding the election after a tie in the Electoral College between Jefferson and Aaron Burr. Jefferson's triumph was also driven by the strong support he received from states such as New York and Pennsylvania, and the growing public desire for political reform, as reflected in the revolutionary sentiment of the times. The election demonstrated a peaceful transfer of power between political parties, emphasizing Jefferson's victory as a pivotal moment of change in America's government philosophy. These are captured succinctly as (a) Adam's falling support and the House of Representatives electing him on the thirty-sixth ballot, (b) the boost provided by Jeffersonians and Hamilton's attacks on Adams.