To simplify the expression \( 3(4^2 + 32 \div 4 - 5) \), we need to evaluate \( 32 \div 4 \).
Calculating \( 32 \div 4 \):
\[ 32 \div 4 = 8 \]
Now we can replace \( 32 \div 4 \) in the expression:
\[ 3(4^2 + 8 - 5) \]
So, the quotient that must be found to simplify the expression is \( 32 \div 4 \).