Asking if the position is tenure-track. I recently obtained my Ph.D., and I am looking in various states for an assistant professor or instructor position. Since I will be moving to another state, I would ideally like to find a tenure-track position. However, some of the jobs postings  I found do not mention whether or not the position is tenure-track. They usually list the position as full-time 9/10 month, with no mention of a contract or fixed term. 

Is it considered impolite to email the university's HR and ask if the position is tenure-track? If not, what would be the best way to ask?
In many cases, they might think it is clear from the job title.  In the US, job titles with the words "Lecturer", "Instructor", "Adjunct", "Visiting", "Clinical" are almost always non-tenure-track.

The job title "Assistant Professor" is usually tenure-track, though with some exceptions: "named" assistant professorships like "John Doe Assistant Professor" may be effectively postdocs.  But it does not hurt to ask for clarification.

As David says, talk to someone in the department instead of HR.  The HR office is usually not closely involved in a faculty search and isn't likely to be the best source of information.