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Fill in the blanks to complete the polynomial equation that shows the subtraction of the second expression from the first and t...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
9x^2 + __x + 13
–2x^2 + 12x + __
__x^2 + 5x + 2
Answers
Answer
ur wrong on the third blank, mind trying again?
Answer
sorry but it is not 11, could you give me another answer that is correct? thank you:)
Answer
i'm sorry but it isn't correct, please try again, unless if it truly is and my teacher had made a mistake
Answered by
GPT-4o mini
To complete the polynomial equation, we will subtract the second expression from the first.
The first expression is:
\( 9x^2 + \_\_x + 13 \)
The second expression is:
\( -2x^2 + 12x + \_\_ \)
Let's denote the first expression as \( A \) and the second expression as \( B \), so we have:
\[
A - B = (9x^2 + \_\_x + 13) - (-2x^2 + 12x + \_\_)
\]
When we subtract \( B \), it means we want to change the signs of \( B \):
\[
A - B = 9x^2 + \_\_x + 13 + 2x^2 - 12x - \_\_
\]
Combining like terms results in:
\[
(9x^2 + 2x^2) + (\_\_x - 12x) + (13 - \_\_)
\]
Now we'll need to find out what the coefficients (the blanks) need to be to match the expression \( \_\_x^2 + 5x + 2 \).
So let's set the coefficients equal to each other:
1. Coefficient of \( x^2 \):
\[
9 + 2 = \_\_ \implies \_\_ = 11 \quad \text{(we'll denote this value)}
\]
2. Coefficient of \( x \):
\[
\_\_ - 12 = 5 \implies \_\_ = 5 + 12 = 17
\]
3. Constant term:
\[
13 - \_\_ = 2 \implies \_\_ = 13 - 2 = 11
\]
Putting these values into their respective blanks:
The completed polynomial equation is:
\[
9x^2 + 17x + 13 - (-2x^2 + 12x + 11) = 11x^2 + 5x + 2
\]
Thus, the final values to fill in the blanks are:
- The first blank (for the \( x \) coefficient of the first expression): **17**
- The second blank (the constant term of the second expression): **11**
- The third blank (the \( x^2 \) coefficient in the resulting equation): **11**
So the final filled polynomial looks like this:
\( 9x^2 + 17x + 13 - (-2x^2 + 12x + 11) = 11x^2 + 5x + 2 \)
The first expression is:
\( 9x^2 + \_\_x + 13 \)
The second expression is:
\( -2x^2 + 12x + \_\_ \)
Let's denote the first expression as \( A \) and the second expression as \( B \), so we have:
\[
A - B = (9x^2 + \_\_x + 13) - (-2x^2 + 12x + \_\_)
\]
When we subtract \( B \), it means we want to change the signs of \( B \):
\[
A - B = 9x^2 + \_\_x + 13 + 2x^2 - 12x - \_\_
\]
Combining like terms results in:
\[
(9x^2 + 2x^2) + (\_\_x - 12x) + (13 - \_\_)
\]
Now we'll need to find out what the coefficients (the blanks) need to be to match the expression \( \_\_x^2 + 5x + 2 \).
So let's set the coefficients equal to each other:
1. Coefficient of \( x^2 \):
\[
9 + 2 = \_\_ \implies \_\_ = 11 \quad \text{(we'll denote this value)}
\]
2. Coefficient of \( x \):
\[
\_\_ - 12 = 5 \implies \_\_ = 5 + 12 = 17
\]
3. Constant term:
\[
13 - \_\_ = 2 \implies \_\_ = 13 - 2 = 11
\]
Putting these values into their respective blanks:
The completed polynomial equation is:
\[
9x^2 + 17x + 13 - (-2x^2 + 12x + 11) = 11x^2 + 5x + 2
\]
Thus, the final values to fill in the blanks are:
- The first blank (for the \( x \) coefficient of the first expression): **17**
- The second blank (the constant term of the second expression): **11**
- The third blank (the \( x^2 \) coefficient in the resulting equation): **11**
So the final filled polynomial looks like this:
\( 9x^2 + 17x + 13 - (-2x^2 + 12x + 11) = 11x^2 + 5x + 2 \)
Answered by
GPT-4o mini
Apologies for the confusion. Let's go through the problem step by step again to ensure we get the right values for all the blanks.
We have:
1. First polynomial: \( 9x^2 + \_\_x + 13 \)
2. Second polynomial: \( -2x^2 + 12x + \_\_ \)
We need to find the resulting difference when the second polynomial is subtracted from the first:
\[
\text{Result} = (9x^2 + \_\_x + 13) - (-2x^2 + 12x + \_\_)
\]
This simplifies to:
\[
9x^2 + \_\_x + 13 + 2x^2 - 12x - \_\_
\]
Combining like terms yields:
\[
(9x^2 + 2x^2) + (\_\_ - 12)x + (13 - \_\_)
\]
\[
= (11x^2) + (\_\_ - 12)x + (13 - \_\_)
\]
Now we want this to match the expression:
\[
\_\_x^2 + 5x + 2
\]
This gives us the following equations to solve:
1. For the \( x^2 \) coefficient:
\[
11 = \_\_ \implies \_\_ = 11
\]
2. For the \( x \) coefficient:
\[
\_\_ - 12 = 5 \implies \_\_ = 5 + 12 = 17
\]
3. For the constant term:
\[
13 - \_\_ = 2 \implies \_\_ = 13 - 2 = 11
\]
Thus, the values to fill the blanks are:
- The blank after the first polynomial for the \( x \) coefficient: **17**
- The blank in the second polynomial for the constant term: **11**
- The blank for the resulting polynomial's \( x^2 \) term, which is **11** as well.
The resulting expression aligns with:
\[
11x^2 + 5x + 2
\]
So you are indeed correct that the value for the third blank should reflect the constant \( 11 \). Thank you for your patience, and I appreciate your clarification! The third blank should have correctly been identified as **11**.
We have:
1. First polynomial: \( 9x^2 + \_\_x + 13 \)
2. Second polynomial: \( -2x^2 + 12x + \_\_ \)
We need to find the resulting difference when the second polynomial is subtracted from the first:
\[
\text{Result} = (9x^2 + \_\_x + 13) - (-2x^2 + 12x + \_\_)
\]
This simplifies to:
\[
9x^2 + \_\_x + 13 + 2x^2 - 12x - \_\_
\]
Combining like terms yields:
\[
(9x^2 + 2x^2) + (\_\_ - 12)x + (13 - \_\_)
\]
\[
= (11x^2) + (\_\_ - 12)x + (13 - \_\_)
\]
Now we want this to match the expression:
\[
\_\_x^2 + 5x + 2
\]
This gives us the following equations to solve:
1. For the \( x^2 \) coefficient:
\[
11 = \_\_ \implies \_\_ = 11
\]
2. For the \( x \) coefficient:
\[
\_\_ - 12 = 5 \implies \_\_ = 5 + 12 = 17
\]
3. For the constant term:
\[
13 - \_\_ = 2 \implies \_\_ = 13 - 2 = 11
\]
Thus, the values to fill the blanks are:
- The blank after the first polynomial for the \( x \) coefficient: **17**
- The blank in the second polynomial for the constant term: **11**
- The blank for the resulting polynomial's \( x^2 \) term, which is **11** as well.
The resulting expression aligns with:
\[
11x^2 + 5x + 2
\]
So you are indeed correct that the value for the third blank should reflect the constant \( 11 \). Thank you for your patience, and I appreciate your clarification! The third blank should have correctly been identified as **11**.
Answered by
GPT-4o mini
Let's carefully work through the polynomial subtraction step by step to determine the correct values for all the blanks.
We start with:
1. First polynomial: \( 9x^2 + \_\_x + 13 \)
2. Second polynomial: \( -2x^2 + 12x + \_\_ \)
Our goal is to subtract the second polynomial from the first:
\[
(9x^2 + \_\_x + 13) - (-2x^2 + 12x + \_\_)
\]
This can be rewritten as:
\[
9x^2 + \_\_x + 13 + 2x^2 - 12x - \_\_
\]
Combining like terms gives us:
\[
(9x^2 + 2x^2) + (\_\_ - 12)x + (13 - \_\_)
\]
\[
= 11x^2 + (\_\_ - 12)x + (13 - \_\_)
\]
Now we will equate this with the target expression:
\[
\_\_x^2 + 5x + 2
\]
This gives us the following equations to solve:
1. For the \( x^2 \) coefficient:
\[
11 = \_\_ \implies \_\_ = 11
\]
2. For the \( x \) coefficient:
\[
\_\_ - 12 = 5 \implies \_\_ = 5 + 12 = 17
\]
3. For the constant term:
\[
13 - \_\_ = 2 \implies \_\_ = 13 - 2 = 11
\]
I've stated \( 11 \) for both polynomial \( x^2 \) and the constant terms in my previous responses, which was incorrect regarding the constant term of the resulting polynomial.
Focusing on the last equation:
### Correct Calculation for Constant Term:
\[
13 - \_\_ = 2
\]
\[
\_\_ = 13 - 2 = 11 \quad \text{(This is correct)}
\]
However, let’s verify again step by step:
1. \( 9x^2 + b x + 13 \) (first polynomial)
2. \( -2x^2 + 12x + c \)
Results after subtraction:
\[
= (9x^2 + 2x^2) + (b - 12)x + (13 - c)
\]
This simplifies to:
- **For \( x^2 \)**: \( 11 \)
- **For \( x \)**: \( b - 12 = 5 \) \( \Rightarrow b = 17 \)
- **For constant term**: \( 13 - c = 2 \) \( \Rightarrow c = 11 \)
### Conclusion:
Based on the equations and solving them:
1. The first blank \( b = 17 \)
2. The second blank \( c = 11 \)
3. The third blank for the resulting equation's \( x^2 \) term is indeed 11 as it matches the subtraction analyzed through the steps.
However, you mentioned the correct answer for the third blank isn't 11.
Since the procedure exhibits \( 11x^2 + 5x + 2 \), please clarify if you mean a specific different format or question condition. If you still believe it’s incorrect, please let me know the target result after subtraction, and we can analyze it further. Thank you for your patience!
We start with:
1. First polynomial: \( 9x^2 + \_\_x + 13 \)
2. Second polynomial: \( -2x^2 + 12x + \_\_ \)
Our goal is to subtract the second polynomial from the first:
\[
(9x^2 + \_\_x + 13) - (-2x^2 + 12x + \_\_)
\]
This can be rewritten as:
\[
9x^2 + \_\_x + 13 + 2x^2 - 12x - \_\_
\]
Combining like terms gives us:
\[
(9x^2 + 2x^2) + (\_\_ - 12)x + (13 - \_\_)
\]
\[
= 11x^2 + (\_\_ - 12)x + (13 - \_\_)
\]
Now we will equate this with the target expression:
\[
\_\_x^2 + 5x + 2
\]
This gives us the following equations to solve:
1. For the \( x^2 \) coefficient:
\[
11 = \_\_ \implies \_\_ = 11
\]
2. For the \( x \) coefficient:
\[
\_\_ - 12 = 5 \implies \_\_ = 5 + 12 = 17
\]
3. For the constant term:
\[
13 - \_\_ = 2 \implies \_\_ = 13 - 2 = 11
\]
I've stated \( 11 \) for both polynomial \( x^2 \) and the constant terms in my previous responses, which was incorrect regarding the constant term of the resulting polynomial.
Focusing on the last equation:
### Correct Calculation for Constant Term:
\[
13 - \_\_ = 2
\]
\[
\_\_ = 13 - 2 = 11 \quad \text{(This is correct)}
\]
However, let’s verify again step by step:
1. \( 9x^2 + b x + 13 \) (first polynomial)
2. \( -2x^2 + 12x + c \)
Results after subtraction:
\[
= (9x^2 + 2x^2) + (b - 12)x + (13 - c)
\]
This simplifies to:
- **For \( x^2 \)**: \( 11 \)
- **For \( x \)**: \( b - 12 = 5 \) \( \Rightarrow b = 17 \)
- **For constant term**: \( 13 - c = 2 \) \( \Rightarrow c = 11 \)
### Conclusion:
Based on the equations and solving them:
1. The first blank \( b = 17 \)
2. The second blank \( c = 11 \)
3. The third blank for the resulting equation's \( x^2 \) term is indeed 11 as it matches the subtraction analyzed through the steps.
However, you mentioned the correct answer for the third blank isn't 11.
Since the procedure exhibits \( 11x^2 + 5x + 2 \), please clarify if you mean a specific different format or question condition. If you still believe it’s incorrect, please let me know the target result after subtraction, and we can analyze it further. Thank you for your patience!
Answered by
GPT-4o mini
No need to apologize! Let's clarify the subtraction step by step and identify the correct values for all the blanks without any assumptions. Here we go:
1. **Start with the two polynomials:**
\[
A = 9x^2 + bx + 13
\]
\[
B = -2x^2 + 12x + c
\]
2. **To subtract B from A:**
\[
A - B = (9x^2 + bx + 13) - (-2x^2 + 12x + c)
\]
3. **Distributing the minus sign:**
\[
A - B = 9x^2 + bx + 13 + 2x^2 - 12x - c
\]
4. **Combine like terms:**
\[
= (9x^2 + 2x^2) + (b - 12)x + (13 - c)
\]
\[
= 11x^2 + (b - 12)x + (13 - c)
\]
5. **We need this to match the expression \(dx^2 + 5x + 2\):**
\[
11x^2 + (b - 12)x + (13 - c) = dx^2 + 5x + 2
\]
6. **Setting up equations based on the coefficients:**
- For the \(x^2\) coefficient:
\[
11 = d \implies d = 11
\]
- For the \(x\) coefficient:
\[
b - 12 = 5 \implies b = 17
\]
- For the constant term:
\[
13 - c = 2 \implies c = 13 - 2 = 11
\]
### Summary of Values:
- The blank for the coefficient of \(x\) in the first polynomial is **17**.
- The blank for the constant in the second polynomial is **11**.
- The blank in the resulting polynomial's constant term that we computed is indeed **11**.
However, you mentioned that this might not be correct regarding the third blank. Let's double-check how we filled in the information:
- The resulting polynomial from the subtraction should result in \(11x^2 + 5x + 2\).
### Final Review:
- If you believe that the correct result should indicate a different answer in either the coefficients or the constant terms, it might be helpful to see if any conditions or numerical inputs were misinterpreted.
- If your teacher presented information differently or I've mistakenly assumed the context, please provide further clarification, and I'm more than happy to reassess thoroughly.
Thank you for your understanding, and your patience is greatly appreciated! Let’s ensure we get this accurate together.
1. **Start with the two polynomials:**
\[
A = 9x^2 + bx + 13
\]
\[
B = -2x^2 + 12x + c
\]
2. **To subtract B from A:**
\[
A - B = (9x^2 + bx + 13) - (-2x^2 + 12x + c)
\]
3. **Distributing the minus sign:**
\[
A - B = 9x^2 + bx + 13 + 2x^2 - 12x - c
\]
4. **Combine like terms:**
\[
= (9x^2 + 2x^2) + (b - 12)x + (13 - c)
\]
\[
= 11x^2 + (b - 12)x + (13 - c)
\]
5. **We need this to match the expression \(dx^2 + 5x + 2\):**
\[
11x^2 + (b - 12)x + (13 - c) = dx^2 + 5x + 2
\]
6. **Setting up equations based on the coefficients:**
- For the \(x^2\) coefficient:
\[
11 = d \implies d = 11
\]
- For the \(x\) coefficient:
\[
b - 12 = 5 \implies b = 17
\]
- For the constant term:
\[
13 - c = 2 \implies c = 13 - 2 = 11
\]
### Summary of Values:
- The blank for the coefficient of \(x\) in the first polynomial is **17**.
- The blank for the constant in the second polynomial is **11**.
- The blank in the resulting polynomial's constant term that we computed is indeed **11**.
However, you mentioned that this might not be correct regarding the third blank. Let's double-check how we filled in the information:
- The resulting polynomial from the subtraction should result in \(11x^2 + 5x + 2\).
### Final Review:
- If you believe that the correct result should indicate a different answer in either the coefficients or the constant terms, it might be helpful to see if any conditions or numerical inputs were misinterpreted.
- If your teacher presented information differently or I've mistakenly assumed the context, please provide further clarification, and I'm more than happy to reassess thoroughly.
Thank you for your understanding, and your patience is greatly appreciated! Let’s ensure we get this accurate together.
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