How/Why did the annexation of Mexican territory push the united states closer to the civil war?

When James K. Polk ran for president in 1844, he ran on a platform of expansion, specifically promising to secure US claims to the Oregon Territory and to annex Texas, California, and New Mexico. From 1846 to 1848, the US fought Mexico in the Mexican-American War, and the Treaty of Guadalupe-Hidalgo, signed in 1848, granted the US 525,000 square miles of former Mexican territory, including present-day California, Arizona, New Mexico, Colorado, Nevada, Utah, and Wyoming. However, these new acquisitions reignited the long-standing issue of slavery in the United States, specifically the question of whether slavery would be allowed to spread into territories that could one day become states. Since the Constitutional Convention in 1787 and with passage of the Missouri Compromise in 1820, political leaders sought to maintain a balance between free states and slave states in Congress. Adding the new territory from the Mexican-American War opened the opportunity for additional free or slave states to enter the Union. Southerners and pro-slavery Congressmen argued that slavery should not be prohibited anywhere, whereas Northerners and opponents of slavery and its spread argued that slavery should not be allowed in new territories.
This issue came to a head when California applied for statehood as a free state in 1849, threatening to upset the balance between free and slave states. Senator Henry Clay brokered a compromise that revealed the increasing tensions between North and South and free and slave states. California entered the Union as a free state, but in Utah and New Mexico, residents would choose whether or not to allow slavery (it would be decided by popular sovereignty). In addition, the slave trade was outlawed in Washington, DC, and a stricter Fugitive Slave Law was passed. While this compromise temporarily settled the issue, it would reemerge by 1854, when the Kansas-Nebraska Act was passed.