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) 9x2 + x + 13 – 2x2 + 12x + x2 + 5x + 2

Answer 1

That is incorrect

Answer 2

That is the same answer, it is incorrect.

Answer 3

It's still incorrect!!

Answer 4

To complete the polynomial equation showing the subtraction of the second expression from the first, we start with the given expression:

The first expression is:
\[ 9x^2 + x + 13 \]

The second expression is:
\[ 2x^2 + 12x + x^2 + 5x + 2 \]

First, we combine like terms in the second expression:
\[ 2x^2 + x^2 = 3x^2 \]
\[ 12x + 5x = 17x \]

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

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

This results in:
1. Subtract the \(x^2\) terms:
\[ 9x^2 - 3x^2 = 6x^2 \]

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

3. Subtract the constant terms:
\[ 13 - 2 = 11 \]

Putting it all together, the final expression after the subtraction is:
\[ 6x^2 - 16x + 11 \]

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

Answer 5

Let's carefully go through the subtraction step by step again.

We start with the expressions provided:

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

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

First, let's combine like terms in the second expression:

- Combine \(2x^2\) and \(x^2\):
\[ 2x^2 + x^2 = 3x^2 \]

- Combine \(12x\) and \(5x\):
\[ 12x + 5x = 17x \]

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

Now we perform the subtraction:

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

Now we subtract each corresponding term:

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

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

3. For constant terms:
\[
13 - 2 = 11
\]

Putting it all together, we have:
\[
6x^2 - 16x + 11
\]

So the correctly completed polynomial equation showing the subtraction of the second expression from the first is:

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

Please let me know if this explanation clarifies the process or if you have further questions.

Answer 6

I apologize for the confusion earlier. Let's reevaluate the problem step by step to ensure we arrive at the correct answer.

We have the following expressions:

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

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

**Step 1: Combine like terms in the second expression.**
- For the \(x^2\) terms:
\[ 2x^2 + x^2 = 3x^2 \]

- For the \(x\) terms:
\[ 12x + 5x = 17x \]

- The constant term is:
\[ 2 \]

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

**Step 2: Perform the subtraction.**
Now we will subtract the second expression from the first:

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

**Distributing the negative sign across the second expression:**

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

**Step 3: Combine like terms.**

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

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

- For the constant terms:
\[ 13 - 2 = 11 \]

Putting it all together, we get:

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

**Final Result:**

The correct subtraction statement is:

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

If you have an alternative expression or requirement that I'm missing, please clarify, and I'll be glad to assist!

Answer 7

Apologies for the misunderstanding. Let's work through the problem from the beginning again with careful attention to all details.

Given expressions:

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

2. **Second expression:**
\[ 2x^2 + 12x + x^2 + 5x + 2 \]

### Step 1: Combine like terms in the second expression.

Let’s simplify the second expression:

- Combine \(2x^2\) and \(x^2\):
\[
2x^2 + 1x^2 = 3x^2
\]

- Combine \(12x\) and \(5x\):
\[
12x + 5x = 17x
\]

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

### Step 2: Subtract the second expression from the first.

Now we need to subtract the second expression from the first:
\[
(9x^2 + x + 13) - (3x^2 + 17x + 2)
\]

### Step 3: Distribute the negative sign.

This gives us:
\[
9x^2 + x + 13 - 3x^2 - 17x - 2
\]

### Step 4: Combine like terms.

Now, let's combine the terms together:

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

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

3. **For constants:**
\[
13 - 2 = 11
\]

Putting all these together, we have:
\[
6x^2 - 16x + 11
\]

### Summary of the polynomial equation:
Thus, the complete polynomial equation that shows the subtraction of the second expression from the first is:
\[
9x^2 + x + 13 - (3x^2 + 17x + 2) = 6x^2 - 16x + 11
\]

If there's an error in understanding the expressions or any specific details, please clarify. Thank you for your patience!