Final answer:
President Polk aimed for a limited war with Mexico, focusing on the conquest of California and New Mexico, aligned with the principles of manifest destiny. The correct answer is option a. and c.
Step-by-step explanation:
When the war with Mexico began, President James K. Polk did not advocate for taking all of Mexico nor did he believe the British would intervene on behalf of the Americans. Instead, President Polk hoped to fight a limited war, aiming for the conquest of California and New Mexico. Polk's actions were driven by the concept of manifest destiny, the belief in the United States' divine right to expand across the continent. Polk attempted to purchase these territories from Mexico first but was prepared to use force if necessary, sending troops into disputed territories and responding forcefully when skirmishes broke out, ultimately leading to the Mexican-American War.