To simplify the expression \( 3(4^2 + 32 \div 4 - 5) \), we need to find the quotient for the division part of the expression.
The division part of the expression is \( 32 \div 4 \).
So, the quotient that must be found is \( 32 \div 4 \), which equals \( 8 \).
Thus, the quotient that must be found to simplify the expression is \( 8 \).