How many auxiliary verbs does the sentence below have?

Solution 1:

"The homework has been completed"

There are two auxiliary verbs but they are auxiliary to different verbs!

1. The verb "to be" forms the passive voice in English. This is an auxiliary verb that affects the verb "to complete". Thus the active verb "to complete" has the passive form "to be completed"

2. The verb "to have" forms the present perfect in English. In this particular case, the verb "to have" is an auxiliary of the verb "to be".

Thus:

"to have been completed" is the present perfect passive (infinitive) of the verb "to complete".

In this case, "have" is auxiliary to "been" and "been" is auxiliary to "completed".

Does that explain it?