Why did divisions in the republican party occur? because the national progressive party was formed by a woman because there was a majority in both house and senate due to the landslide defeat to lyndon johnson because conservative republicans re-elected taft at the party's 1912 national convention

Answer is: because conservative Republicans re-elected Taft at the party's 1912 national convention.
1912 National Convention of the Republican Party of the United States was held at Chicago. That was beginning of a split in the party because a power struggle between Taft and former president Theodore Roosevelt.  Roosevelt as defeted established new Progressive Party.