Final answer:
The availability of gold and silver most strongly encouraged settlement of the West in the late 1800s.
Step-by-step explanation:
The factor that most strongly encouraged settlement of the West in the late 1800s was the availability of gold and silver (option a). The California Gold Rush in 1849 attracted thousands of miners looking to strike it rich quickly. The discovery of precious metals, along with the completion of the Transcontinental Railroad in 1869, pushed the settlement frontier westward and fueled the desire for wealth and opportunity.