Final answer:
The passage directly supports the idea that Mexico had loose control over its northern territories, as Texas and California became independent and then were annexed by the United States despite being part of Mexico.
Step-by-step explanation:
The passage supports the assertion that Mexico did not have very tight control over its northern territories in California and Texas. This is demonstrated by the fact that many people settled in these territories during the 1820s and 1830s, and despite the territories being officially a part of Mexico, they eventually became independent and subsequently were annexed by the United States. Furthermore, the passage indicates that the settlers and American expansionists had goals at odds with Mexico's sovereignty, such as the declaration of Texas's independence, and President Polk's desire to acquire additional Mexican lands, ultimately leading to the Mexican-American War and the significant loss of Mexican territory.