To fill in the blanks, we need to set up the subtraction of the second polynomial from the first polynomial and also show the resulting difference.
### Starting Polynomial Expressions
1. **First Polynomial (Expression 1)**:
\( 9x^2 + x + 13 \)
2. **Second Polynomial (Expression 2)**:
\( 2x^2 - 12x - (x^2 + 5x + 2) \)
Let's correctly set this up step-by-step:
### Step 1: Formatting the Equation
To subtract the second polynomial, we rewrite it such that we switch the signs of the terms in the second polynomial:
\[
(9x^2 + x + 13) - (2x^2 + 12x + (x^2 + 5x + 2))
\]
This can also be rephrased as:
\[
(9x^2 + x + 13) - (2x^2 + 12x + 2x^2 + 5x + 2)
\]
### Step 2: Combine the Terms
Let's simplify this equation:
1. Combine the second polynomial:
\[
2x^2 + 12x + 2
\]
### Step 3: Writing the Final Polynomial
We can now set it up in blanks as requested:
1. The first polynomial is \( 9x^2 \).
2. The second polynomial is \( 2x^2 + 12x + 2 \).
Thus the entire setup will be:
\[
9x^2 + x + 13 - (2x^2 + 12x + 2) = (9x^2 - 2x^2) + (x - 12x) + (13 - 2)
\]
### Step 4: Calculation of the Resulting Difference
Now calculating the resulting differences:
- Quadratic terms: \( 9x^2 - 2x^2 = 7x^2 \)
- Linear terms: \( x - 12x = -11x \)
- Constant terms: \( 13 - 2 = 11 \)
Thus the final expression becomes:
### Final Result
The resulting polynomial expression is:
\[
7x^2 - 11x + 11
\]
### Filling in the Blanks
Given these details, here is how you might fill in the blanks:
- First blank (first polynomial, \(9x^2\)): **\(9x^2\)**
- Second blank (linear term, \(x\)): **\(x\)**
- Third blank (constant term, \(13\)): **\(13\)**
- Fourth blank (for \(12x\)): **\(12x\)**
- Fifth blank (constant term, \(2\)): **\(2\)**
So the completed equation with blanks would be:
\[
9x^2 + x + 13 - (2x^2 + 12x + 2)
\]
Resulting in the difference:
\[
= 7x^2 - 11x + 11
\]
If there are any adjustments needed based on the blanks provided in the original prompt, please let me know!