Which factor plays a central role in determining which of the brain's synapses will be eliminated and which will be maintained?

The answer is "frequency with which they are activated".

Explanation:

Frequency refers to the number of consecutive repetitive events per unit time. It is measured in hertz (Hz), equivalent to a single event per second. The time is the number of one cycle in a recurrent event, and so the duration is the same for the frequency, hence the frequency at which they are triggered is a key determinant of the brain's connections to be eliminated and maintained.

a- all cells come from pre-existing cells