Final answer:
Alexander Borodin composed the opera Prince Igor which contains the "Polovetsian Dances", not Igor Stravinsky. The dances are frequently performed as an orchestral suite, separate from the opera.
Step-by-step explanation:
The opera Prince Igor, which features the renowned "Polovetsian Dances", was composed by Alexander Borodin, not Igor Stravinsky.
Although Stravinsky is a famous Russian composer known for The Rite of Spring, the Polovetsian Dances come from a different composer's opera.
Borodin's opera, Prince Igor, was indeed completed posthumously by his contemporaries Rimsky-Korsakov and Glazunov. It is Borodin's work that includes these famous dances, which can often be heard performed separately as an orchestral suite in concerts.