To simplify the expression \(3(4^2 + 32 \div 4 - 5)\), we first need to evaluate the parts inside the parentheses.
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Calculate \(4^2\): \[ 4^2 = 16 \]
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Calculate \(32 \div 4\): \[ 32 \div 4 = 8 \]
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Now, substitute these values back into the expression inside the parentheses: \[ 3(16 + 8 - 5) \]
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Next, simplify inside the parentheses: \[ 16 + 8 = 24 \] \[ 24 - 5 = 19 \]
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Finally, we have: \[ 3(19) \]
In order to simplify the original expression, the quotient we needed to find is \(32 \div 4\).
Therefore, to properly simplify the given expression, the quotient is: \[ \boxed{8} \]