To fill in the blanks, we start with the given polynomial expressions and perform the subtraction step-by-step.
The first expression is:
\[ 9x^2 + x + 13 \]
The second expression is:
\[ 2x^2 + 12x + \text{(blank)} \]
The third expression is:
\[ x^2 + 5x + 2 \]
We need to subtract the sum of the second and third expressions from the first expression.
Let's first find the sum of the second and third expressions:
\[
(2x^2 + 12x + \text{(blank)}) + (x^2 + 5x + 2)
\]
Which simplifies to:
\[
(2x^2 + x^2) + (12x + 5x) + (\text{(blank)} + 2) = 3x^2 + 17x + (\text{(blank)} + 2)
\]
Next, we need to perform the subtraction:
\[
(9x^2 + x + 13) - (3x^2 + 17x + (\text{(blank)} + 2))
\]
Now, let's distribute the negative sign:
\[
9x^2 + x + 13 - 3x^2 - 17x - (\text{(blank)} + 2)
\]
Combining like terms gives:
\[
(9x^2 - 3x^2) + (x - 17x) + (13 - (\text{(blank)} + 2)) = 6x^2 - 16x + (13 - \text{(blank)} - 2)
\]
Simplifying further, we have:
\[
= 6x^2 - 16x + (11 - \text{(blank)})
\]
From the equation provided, we can see that we need to identify the term that would balance this subtraction. Thus:
\[
\text{(blank)} = 11
\]
Accordingly, the filled polynomial equation is:
\[
9x^2 + x + 13 - (2x^2 + 12x + 11) - (x^2 + 5x + 2)
\]
So if we refill the blanks, we have:
\[
9x^2 + x + 13 - 2x^2 + 12x + 11
\]
Therefore:
\[
\text{blank} = 11
\]
And, thus, we finish with:
**Resulting difference:**
\[ 6x^2 - 16x + 9 \] (where the constant term comes from taking 11 from 11, summing these up as previously described).