To complete the polynomial equation by subtracting the second expression from the first, let's break down the provided expressions.
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Original expression: \[ 9x^2 + x + 13 \]
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Expression to subtract: \[ 2x^2 + 12x + ___ \]
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The third expression given is: \[ x^2 + 5x + 2 \]
Now we can rewrite the subtraction: \[ (9x^2 + x + 13) - (2x^2 + 12x + ___) \]
To find the blank (the term that will complete the expression), we need to focus on what follows. The expected difference must incorporate all relevant components from the subtraction operation.
Performing the subtraction:
Let's assume the second polynomial needs to be correctly represented as: \[ 2x^2 + 12x + C \] where C is the missing constant.
Now subtract this from the first polynomial:
- Subtracting \(2x^2\): \[ 9x^2 - 2x^2 = 7x^2 \]
- Subtracting \(12x\): \[ x - 12x = -11x \]
- Subtracting the missing constant \(C\): \[ 13 - C \]
Resulting expression:
Combining all the results gives us the subtraction: \[ 7x^2 - 11x + (13 - C) \]
Final Construction:
Assuming the last polynomial given \(x^2 + 5x + 2\) signifies what we should expect at the end implies that \(C\) supports or relates to that constant.
To return to that format (looking for constant) and equate it for context, we can assume \(C\) is \(0\) leading us to focus purely on the polynomial results.
Thus, filling in: The polynomial subtraction format looks established once we arrive at the correct results without conflicting misconceptions presented with conflicting orders.
Final result to fill in the blank: Since the last provided polynomial indicates a final \(C\) form as \(2\) leading the expectation while also `influencing placement` the final polynomial can expand or reflect supporting terms accordingly.
The missing term in this context provides clarity recognizing values and adjustments:
So, the polynomial subtraction becomes: \[ 7x^2 - 11x + (13 - 2) \Rightarrow (7x^2 - 11x + 11) \] confirming simplistically the blank is: \[ \boxed{2} \]
Thus the complete subtraction yields \[ 9x^2 + x + 13 - (2x^2 + 12x + 2) \Rightarrow 7x^2 - 11x + 11 \]