Fill in the blanks to complete the polynomial equation that shows the subtraction of the second expression from the first and the resulting difference. (2 points)

To fill in the blanks for the polynomial equation that shows the subtraction of the second expression from the first, let's rewrite the expressions clearly:

First expression:
\[ 9x^2 + x + 13 \]

Second expression:
\[ 2x^2 + 12x + (x^2 + 5x + 2) \]

Now, we need to perform the subtraction:

\[ (9x^2 + x + 13) - (2x^2 + 12x + x^2 + 5x + 2) \]

First, combine the second expression:

\[ 2x^2 + 12x + x^2 + 5x + 2 = (2x^2 + x^2) + (12x + 5x) + 2 \]
\[ = 3x^2 + 17x + 2 \]

Now, we will subtract this combined expression from the first expression:

\[ 9x^2 + x + 13 - (3x^2 + 17x + 2) \]

Distributing the negative sign gives:

\[ 9x^2 + x + 13 - 3x^2 - 17x - 2 \]

Now combine like terms:

- For \(x^2\) terms: \(9x^2 - 3x^2 = 6x^2\)
- For \(x\) terms: \(x - 17x = -16x\)
- For constant terms: \(13 - 2 = 11\)

Putting it all together, we have:

\[ 6x^2 - 16x + 11 \]

Therefore, the original subtraction problem, filled in completely, looks like this:

\[
9x^2 + x + 13 - (2x^2 + 12x + (x^2 + 5x + 2)) = 6x^2 - 16x + 11
\]

So the filled-in blanks would be:

- In the second expression, the blank after \(+ 12x\) should be \(x^2\) (the start of the additional polynomial).
- In that additional polynomial, \(+ 5x\) should have the blank filled with \(2\) (the constant term).

Thus the complete answer is:

1. **Second expression blank:** \(x^2\)
2. **Sum of that additional polynomial blank:** \(2\)