Final answer:
Portugal and Spain were motivated to explore new lands due to a combination of religious conversion, the desire for wealth, and the need to counter the influence of Islam. Both nations sought to spread Christianity and find new trade routes.
Step-by-step explanation:
The motivations for Portugal and Spain to explore new lands were primarily driven by religious conversion and missionary zeal, as well as the desire to acquire wealth and riches. Both nations had a strong Catholic influence and sought to spread Christianity and counter the influence of Islam. They were also driven by the potential economic benefits of finding new trade routes and sources of valuable resources.