When mexico won its independence from spain in 1821, texas was

a spanish colony.

owned by the united states.

an independent nation.

a province of mexico.

Texas was an independent nation, the Republic of Texas until 1845, when it joined the United States.
Therefore, the third option is correct.

The transcontinental railroad provided a means of fast transportation. it cut a 6 month trip into 6 days, created jobs for many people and encouraged immigration. the homestead act played a huge role in western expansion; it allowed settlers to begin a fresh start, and gave them land in exchange for their residence for up to five years and a small fee.