Which of the following was a major factor in the decline of the Byzantine empire?

A. the decision to divide the Roman empire in two
B. the dispute between the pope and the patriarch of Constantinople
C. repeated attacks by Muslim invaders
D. the conquests of Justinian in the West

The correct answer is C. repeated attacks by Muslim invaders.

To figure out the correct answer, you can eliminate the other options by analyzing their historical context and impact on the decline of the Byzantine Empire.

Option A, the decision to divide the Roman Empire in two, refers to the split of the Roman Empire into the Western Roman Empire and the Eastern Roman Empire in 395 AD. This division was not a major factor in the decline of the Byzantine Empire since the Eastern Roman Empire, also known as the Byzantine Empire, continued to exist for another thousand years.

Option B, the dispute between the pope and the patriarch of Constantinople, refers to the Great Schism of 1054, which led to the permanent split between the Eastern Orthodox Church and the Roman Catholic Church. While this event had significant religious and cultural consequences, it was not a primary factor in the decline of the Byzantine Empire.

Option D, the conquests of Justinian in the West, refers to the military campaigns led by Byzantine Emperor Justinian in the 6th century to recapture former Western Roman territories. While these conquests briefly expanded the Byzantine Empire's territory, they were not a major factor in its decline.

Therefore, by process of elimination, the correct answer is C. repeated attacks by Muslim invaders. The repeated invasions by Muslim armies, such as the Arab and Seljuk Turks, put immense pressure on the Byzantine Empire's borders and weakened its defenses over time, ultimately contributing to its decline.