Question

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)
9x^2
+
x + 13
– 2x^2
+ 12x
+

x^2
+ 5x
+ 2

Answer 1

bot are you sure?

Answer 2

bot each equation needs to be separate from each other

Answer 3

To complete the polynomial equation, we will subtract the second expression from the first and determine the resulting difference.

Given the first expression:
\( 9x^2 + x + 13 \)

And the second expression:
\( 2x^2 + 12x + (x^2 + 5x + 2) \)

First, we need to combine the terms of the second expression:

- Combine the \( x^2 \) terms:
- \( 2x^2 + x^2 = 3x^2 \)

- Combine the \( x \) terms:
- \( 12x + 5x = 17x \)

- The constant term remains \( 2 \).

Thus, the second expression simplifies to:
\( 3x^2 + 17x + 2 \)

Now, we can perform the subtraction:
\[
(9x^2 + x + 13) - (3x^2 + 17x + 2)
\]

Distributing the negative sign across the terms of the second expression:
\[
9x^2 + x + 13 - 3x^2 - 17x - 2
\]

Now, combine like terms.
1. For \( x^2 \) terms:
- \( 9x^2 - 3x^2 = 6x^2 \)

2. For \( x \) terms:
- \( x - 17x = -16x \)

3. For constant terms:
- \( 13 - 2 = 11 \)

Therefore, the resulting expression after subtracting is:
\[
6x^2 - 16x + 11
\]

Now we can fill in the blanks:

- The term representing the missing expression after subtraction is \( 3x^2 + 17x + 2 \).
- The resulting difference is \( 6x^2 - 16x + 11 \).

So the completed polynomial equation is:
\[
9x^2 + x + 13 - (3x^2 + 17x + 2) = 6x^2 - 16x + 11
\]

Answer 4

Let’s go through the problem step by step again to ensure accuracy.

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

2. **Second Expression**:
\[
2x^2 + 12x + (x^2 + 5x + 2)
\]

We need to simplify the second expression first:

- Combine \( x^2 \) terms:
\[
2x^2 + x^2 = 3x^2
\]
- Combine \( x \) terms:
\[
12x + 5x = 17x
\]
- The constant term remains \( 2 \).

Therefore, the second expression simplifies to:
\[
3x^2 + 17x + 2
\]

3. **Now we perform the subtraction**:
\[
(9x^2 + x + 13) - (3x^2 + 17x + 2)
\]

When we distribute the negative sign:
\[
9x^2 + x + 13 - 3x^2 - 17x - 2
\]

4. **Combining like terms**:
- For \( x^2 \) terms:
\[
9x^2 - 3x^2 = 6x^2
\]
- For \( x \) terms:
\[
x - 17x = -16x
\]
- For constants:
\[
13 - 2 = 11
\]

Therefore, the final result after performing the subtraction is:
\[
6x^2 - 16x + 11
\]

So the filled in polynomial equation is:
\[
9x^2 + x + 13 - (3x^2 + 17x + 2) = 6x^2 - 16x + 11
\]

This result appears to be accurate based on the calculations provided. If there's anything specific you'd like to clarify or if I misunderstood your question, please let me know!

Answer 5

I understand now that you want the equations separated clearly to show the subtraction process step by step. Let’s format it properly.

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

2. **Second Expression**:
\[
2x^2 + 12x + (x^2 + 5x + 2)
\]

Simplifying the second expression:
- Combine \( x^2 \) terms:
\[
2x^2 + x^2 = 3x^2
\]
- Combine \( x \) terms:
\[
12x + 5x = 17x
\]
- The constant term remains:
\[
+ 2
\]

So the second expression becomes:
\[
3x^2 + 17x + 2
\]

3. **Subtraction Setup**:
We want to subtract the second expression from the first:
\[
(9x^2 + x + 13) - (3x^2 + 17x + 2)
\]

4. **Distributing the Negative Sign**:
\[
9x^2 + x + 13 - 3x^2 - 17x - 2
\]

5. **Combine Like Terms**:
- For \( x^2 \) terms:
\[
9x^2 - 3x^2 = 6x^2
\]
- For \( x \) terms:
\[
x - 17x = -16x
\]
- For the constant terms:
\[
13 - 2 = 11
\]

6. **Final Result**:
Thus, the result of the subtraction is:
\[
6x^2 - 16x + 11
\]

Finally, putting it all together, the filled-in polynomial equation, clearly separated, looks like this:

\[
9x^2 + x + 13
\]
\[
- (3x^2 + 17x + 2)
\]
\[
= 6x^2 - 16x + 11
\]

If this format is what you were looking for, let me know! Thank you for your patience.