Let's analyze the phrase step by step:
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"The product of 3 and a number squared": This can be expressed as \(3x^2\) where \(x\) is the number.
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"minus the product of four and that same number": This can be expressed as \(-4x\).
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"plus 5": This is simply \(+5\).
Now, we can combine these parts to form the complete expression:
\[ 3x^2 - 4x + 5 \]
Thus, the expression that is equivalent to the given phrase is:
C) 3x^2 - 4x + 5.