To simplify the expression \( 3(4^2 + 32 \div 4 - 5) \), we need to handle the division first, according to the order of operations (PEMDAS/BODMAS).
The expression inside the parentheses is: \[ 4^2 + 32 \div 4 - 5 \]
We need to compute \( 32 \div 4 \).
Therefore, the quotient that must be found to simplify the expression is: \[ 32 \div 4 \]
So the correct answer is: C. 32 ÷ 4