Polk was in favor of acquiring both Texas and Oregon because he was a firm believer in manifest destiny.
Manifest destiny is the belief that it is America's god-given right to take over all of the land from the Atlantic to the Pacific Ocean. This belief that it was inevitable that this land would belong to the US prompted the federal government to acquire lands like Texas and Oregon. We acquired Texas after they became free from Mexican rule and we would go on to control a significant amount of the Oregon territory after striking a deal with Great Britain.