What is the purpose of a political party? select all that apply. to gain political power to establish a role in history to recruit any candidate likely to win to promote shared principles and political ideology to endorse candidates who support a specific political philosophy

I would say there are three correct options here. The purpose of a political party is:
to gain political power - this one is self-explanatory; a political party obviously wants to be powerful politically so that it can send one of its members as a presidential candidate, for example; the more power a party has, the more likely it is to attract wide audiences
to help promote shared principles and political ideology - a political party consists of people who share the same beliefs and principles and who want other people outside their party to hear them out and vote for them because they also believe in the same ideology as the party does
to endorse candidates who support a specific political philosophy - again, if a candidate suits the needs of that particular political party, it will be more likely to support him or her and thus endorse them and try to promote them as much as possible so that people will vote for them and make their party an even more powerful one