Parts C and E have errors. In part C, the word 'compounding' is contextually irrelevant to the sentence. The sentence talks about a person who spends more time in a particular state due to the arrival of a new opposition. The appropriate word that matches the context of the sentence is 'campaigning' which means 'work in an organized and active way towards a particular goal, typically a political or social one'. In part E, the adverb 'newly' in incorrectly used to qualify the noun 'opposition', instead the adjective 'new' is to be used.
The correct sentence is: One reason he may have expended so much time and energy campaigning in the state this time could have to do with the arrival of a new opposition party.
Hence, the correct answer is option (e).
Note:
Qualifiers: A word or phrase that limits the meaning of another word or phrase or makes it less general. 'Adverbs' and 'adjectives' are qualifiers.