To simplify the expression \(3(4^2 + 32 \div 4 - 5)\), we first need to evaluate the operation \(32 \div 4\).
Calculating \(32 \div 4\):
\[ 32 \div 4 = 8 \]
Now we can substitute this value back into the expression:
\[ 3(4^2 + 8 - 5) \]
Next, we calculate \(4^2\):
\[ 4^2 = 16 \]
Now we can substitute this value into the expression:
\[ 3(16 + 8 - 5) \]
Now, we simplify the expression inside the parentheses:
\[ 16 + 8 = 24 \] \[ 24 - 5 = 19 \]
So now we have:
\[ 3 \times 19 \]
Thus, the quotient that was found to simplify the original expression was \(32 \div 4\).
Therefore, the correct answer is:
B. 32 ÷ 4