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, 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).

bot the equations need to be separate from each other and be solved separately

Apologies for the confusion earlier. Let's break it down step-by-step and solve each polynomial separately.

Given the following two expressions:

1. **First Expression**:
\[
9x^2 + x + 13
\]

2. **Second Expression**:
\[
2x^2 + 12x + \text{(blank)}
\]

3. **Third Expression**:
\[
x^2 + 5x + 2
\]

We need to find the result of subtracting the second and third expressions from the first.

### Step 1: Find the combined second and third expressions

To do this, we add the second and third expressions:

\[
(2x^2 + 12x + \text{(blank)}) + (x^2 + 5x + 2)
\]

This simplifies to:

\[
(2x^2 + x^2) + (12x + 5x) + (\text{(blank)} + 2) = 3x^2 + 17x + (\text{(blank)} + 2)
\]

### Step 2: Subtract the combined expression from the first expression

Now we can subtract this entire expression from the first expression:

\[
(9x^2 + x + 13) - (3x^2 + 17x + (\text{(blank)} + 2))
\]

### Step 3: Distributing the negative sign

Distributing the negative sign gives us:

\[
9x^2 + x + 13 - 3x^2 - 17x - (\text{(blank)} + 2)
\]

### Step 4: Combine like terms

Now we combine the like terms:

1. **For the \(x^2\) terms**:
\[
9x^2 - 3x^2 = 6x^2
\]

2. **For the \(x\) terms**:
\[
x - 17x = -16x
\]

3. **For the constant terms**:
\[
13 - (\text{(blank)} + 2) = 11 - \text{(blank)}
\]

### Final Result

Putting all of this together, we have:

\[
6x^2 - 16x + (11 - \text{(blank)})
\]

### Step 5: Determine the value for (blank)

To complete the polynomial equation, we need the total to align correctly. For simplicity and based on common constant values:

If we assume that we would like this polynomial to simplify to a common result like \(0\) or another target value.

**Let’s assume we want it zeroed out for a balanced equation**, we would set:

\[
11 - \text{(blank)} = 0 \implies \text{(blank)} = 11
\]

### Conclusion

Thus, the value of \(\text{(blank)}\) is \(11\).

Now, we can rewrite the equation and show each of the pieces separately as follows:

1. **First Expression**:
\[
9x^2 + x + 13
\]

2. **Second Expression**:
\[
2x^2 + 12x + 11
\]

3. **Third Expression**:
\[
x^2 + 5x + 2
\]

And when we calculate:
\[
(9x^2 + x + 13) - (2x^2 + 12x + 11 + x^2 + 5x + 2) \Rightarrow 6x^2 - 16x + 0
\]

This simplifies to:
\[
6x^2 - 16x
\]

If you need to separate the steps further or clarify anything else, please let me know!