Explain the break between William Howard Taft and Theodore Roosevelt, and discuss the impact of this break on the Republican party and on the 1912 presidential election.

The break between William Howard Taft and Theodore Roosevelt occurred during the 1912 presidential election. Roosevelt, who had previously served as president from 1901 to 1909, had handpicked Taft as his successor. However, once in office, Taft's policies and decisions began to diverge from Roosevelt's progressive agenda. This led to a growing rift between the two men, culminating in Roosevelt's decision to challenge Taft for the Republican nomination in the 1912 election.

The impact of this break on the Republican party was significant. The party became deeply divided between the conservative faction supporting Taft and the progressive faction backing Roosevelt. This division ultimately led to a split in the party, with Roosevelt forming the Progressive Party (also known as the Bull Moose Party) and running as its candidate in the election. This split weakened the Republican party and allowed the Democratic candidate, Woodrow Wilson, to win the presidency.

The 1912 presidential election was heavily influenced by the break between Taft and Roosevelt. With the Republican party divided, Wilson was able to secure a decisive victory, winning both the popular vote and the electoral college. This marked the first time in over 20 years that a Democrat had been elected president. The impact of the break between Taft and Roosevelt was therefore significant, not only in terms of the immediate election outcome, but also in shaping the future direction of the Republican party and American politics as a whole.