To simplify the expression \(3(42 + 32 \div 4 - 5)\), we need to perform the division first according to the order of operations (PEMDAS/BODMAS).
The expression inside the parentheses is \(42 + 32 \div 4 - 5\). Therefore, we need to find the quotient \(32 \div 4\).
Thus, the quotient that must be found to simplify the expression is:
32 ÷ 4 (32 divided by 4).