Which political factors influenced the rise of imperialism?

If you mean American imperialism-

The us wanted to expand its influence and find new trading partners and territories in the late 1800s. And hence it's rapid expansion and annexion (claiming rule over) Hawaii.

European imperialism has existed multiple times in history. Between the 15-18th century the likes of Portugal, England, France and Spain engaged in expanding their territories worldwide such as across the americas, India as well as agrica.; paving the way for Britain to establish histories largest empire. World war 1 was characterized by intense imperealism and paved the way for the league of nations (later United Nations) to try and create a better world by which such greed isn't as widespread. And hence, by the mid 20th century, colonization faded steadily.