Answer: (Choice A) A . researched
Explanation:
The word 'extensively' is a degree adverb with a -ly Suffix. To do so something extensively means that a task gets done to a great extent. In this example, it doesn´t refer to either history or French because those are not verbs that can be modified by an adverb. There´s only one verb, 'researched', which can be modified by it. As it´s customarily, the adverb is after the verb that is modifying.