To correctly fill in the blanks for the polynomial equation that shows the subtraction of the second expression from the first, we start with the two expressions provided.
**First Expression:**
\[
9x^2 + x + 13
\]
**Second Expression:**
\[
2x^2 - 12x + (blank\ 1) \\
\]
Now we write the subtraction:
\[
(9x^2 + x + 13) - (2x^2 + 12x + (blank\ 1))
\]
### Steps to Solve:
1. Distribute the negative sign:
\[
9x^2 + x + 13 - 2x^2 - 12x - (blank\ 1)
\]
2. Combine like terms:
- For \(x^2\): \(9x^2 - 2x^2 = 7x^2\)
- For \(x\): \(x - 12x = -11x\)
- For constant: \(13 - (blank\ 1)\)
### Fill in the Blanks:
So, we need **the resulting difference** after performing the subtraction \(9x^2 + x + 13 - (2x^2 + 12x + (blank\ 1))\).
From our earlier calculation, after subtraction, we have:
\[
7x^2 - 11x + (13 - (blank\ 1))
\]
We will assume that the constant from the second polynomial is 0 for the blanks to be filled.
If we want to set the resulting constant term to be equal to 2 (as stated in the question), then we should solve the equation:
\[
13 - (blank\ 1) = 2 \\
(blank\ 1) = 11
\]
### Final polynomial equation filled in:
Putting all the blanks together, we have:
\[
9x^2 + x + 13 - (2x^2 + 12x + 11) = 7x^2 - 11x + 2
\]
### Result
- The blanks to fill are:
1. The first blank should represent the constant from the second expression: **11**
2. Confirming the resulting terms from subtraction, the resulting difference from the first polynomial minus the revised second polynomial would give:
Hence, the complete polynomial equation that shows the subtraction is:
\[
9x^2 + x + 13 - (2x^2 + 12x + 11) = 7x^2 - 11x + 2
\]
Your filled answers will look like this:
- **First Polynomial: \(9x^2\)**
- **x: \(x\)**
- **13: \(13\)**
- **Subtracted: \(2x^2\)**
- **12x: \(12x\)**
- **(Blank for constant): \(11\)** (to represent the constant \(+11\))
- **Resulting \(x^2\): \(7x^2\)**
- **Resulting \(x\): \(-11x\)**
- **Resulting Constant: \(2\)**
Thus, the final polynomial equation is:
\[
9x^2 + x + 13 - (2x^2 + 12x + 11) = 7x^2 - 11x + 2
\]