Final answer:
James K. Polk's campaign slogan that alluded to settling the Oregon Territory was "Fifty-Four Forty or Fight!", referring to the northernmost latitude of the Oregon Territory the U.S. intended to claim. Option b) is the correct answer.
Step-by-step explanation:
James K. Polk's presidential campaign in 1844 was characterized by a strong stance on territorial expansion, particularly regarding the Oregon Territory. The slogan that encapsulated his ambition for settling the Oregon Territory was "Fifty-Four Forty or Fight!", This slogan signaled the United States' intent to take control of the Oregon Country up to the northern latitude of 54 degrees 40 minutes, despite overlapping claims by Great Britain. While Polk publicly supported the aggressive expansionist sentiment, he was ultimately prepared to accept a compromise boundary along the 49th parallel, a pragmatic move that allowed for the acquisition of key territories while avoiding conflict with Britain and preparing for the war with Mexico.