Final answer:
Polk tried to avoid war with Mexico by sending John Slidell to negotiate the purchase of California and New Mexico, but diplomatic efforts failed leading to war.
Step-by-step explanation:
President James K. Polk sought to acquire California and New Mexico without warfare by sending emissary John Slidell with offers to purchase these territories for up to $25 million. Efforts to avoid war and negotiate peacefully included a substantial monetary offer for the purchase of New Mexico and California, but when the Mexican press decried Slidell's mission, it signified a failure of diplomatic resolve.
The mission's revelation and subsequent rejection by Mexico set the stage for Polk to instigate conflict, eventually leading to a formal declaration of war after a skirmish in the disputed territory.