To simplify the expression \( 3(4^2 + 32 \div 4 - 5) \), we need to evaluate the part inside the parentheses.
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Calculate \( 4^2 \): \[ 4^2 = 16 \]
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Now, we need to find \( 32 \div 4 \): \[ 32 \div 4 = 8 \]
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Substituting these values back into the expression, we get: \[ 3(16 + 8 - 5) \]
So, the quotient that must be found to simplify the expression is \( 32 \div 4 \).
Therefore, the correct response is 32 ÷ 4.