Is the word 'request' by itself a polite form of asking for something?

Solution 1:

I request that you . . . is extremely formal, and unlikely to be heard much in speech. Expressions like Could you, please, . . .? and Would you mind . . .? are what are normally used in conversation, and are perfectly polite.

Solution 2:

Politeness depends on more than just language, and so could vary considerably from place to place and context to context.

While it's more polite than the bare form, because it states that it's a request rather than a demand, but not much more.

Really, it's appropriate for legalese where you want to tone things down from an outright demand ("we request that you submit a complaint within 7 days", "we request that you read the terms and conditions before making an order"), but it's not very polite. (You would kindly request someone attend an event in a formal invite, not just request it).

Solution 3:

A request is indeed "An act of asking politely or formally for something."

However, that does not mean the word request must itself be used, and an imperative command sounds less polite than a standard question (with "please" and a question mark).