Final answer:
The adjective clause "that is published by our school" is a restrictive clause, as it provides essential information to define which newspaper is being referred to.
Step-by-step explanation:
The adjective clause in the sentence "The newspaper that is published by our school is quite popular" is a restrictive clause. A restrictive adjective clause is essential to the meaning of the sentence because it specifically restricts or defines the noun it modifies, which in this case is 'the newspaper.' If the clause were removed, the meaning of the sentence would change, suggesting that it is necessary to identify which newspaper we are talking about. Nonrestrictive clauses, on the other hand, simply provide additional information and are not essential to the meaning of the sentence; they can be removed without changing the overall meaning and are typically set off by commas.