问题


There is a single choice question about high school mathematics. Answer the question by replying A, B, C or D.
Question: Simplify the following expression: $(9x^9+7x^8+4x^7) + (x^{11}+x^9+2x^7+3x^3+5x+8).$ Express your answer as a polynomial with the degrees of the terms in decreasing order.
A. x^{11}+2x^9+2x^8
B. x^{11}-6x^8+6x^7+3x^3+5x+8
C. x^11 + 10x^9 + 7x^8+6x^73x^3+5x+8
D. x^{11}+10x^9+7x^8+6x^7+3x^3+5x+8
Answer:

答案

模型 模型答案 正确答案
金声玉亮2.0

D. x^{11}+10x^9+7x^8+6x^7+3x^3+5x+8
D
deepseekr1

To simplify the given expression, combine like terms from both polynomials:

\[
(9x^9 + 7x^8 + 4x^7) + (x^{11} + x^9 + 2x^7 + 3x^3 + 5x + 8)
\]

1. **Combine terms by degree:**
- \(x^{11}\): Only in the second polynomial → \(x^{11}\).
- \(x^9\): \(9x^9 + x^9 = 10x^9\).
- \(x^8\): Only in the first polynomial → \(7x^8\).
- \(x^7\): \(4x^7 + 2x^7 = 6x^7\).
- Lower-degree terms (\(3x^3, 5x, 8\)): Carried over directly.

2. **Arrange in descending order:**
\[
x^{11} + 10x^9 + 7x^8 + 6x^7 + 3x^3 + 5x + 8
\]

3. **Verify answer choices:**
- **A** and **B** omit lower-degree terms or have incorrect coefficients.
- **C** has a typo (\(6x^73x^3\)) and is invalid.
- **D** matches the simplified polynomial.

**Answer: D**
D
gpto1 D D
GPT-4o To simplify the expression \((9x^9+7x^8+4x^7) + (x^{11}+x^9+2x^7+3x^3+5x+8)\), we need to combine like terms.

1. Identify and combine the terms with the same power of \(x\):
- \(x^{11}\) term: \(x^{11}\)
- \(x^9\) terms: \(9x^9 + x^9 = 10x^9\)
- \(x^8\) term: \(7x^8\)
- \(x^7\) terms: \(4x^7 + 2x^7 = 6x^7\)
- \(x^3\) term: \(3x^3\)
- \(x\) term: \(5x\)
- Constant term: \(8\)

2. Write the simplified polynomial with the terms in decreasing order of their degrees:
\[
x^{11} + 10x^9 + 7x^8 + 6x^7 + 3x^3 + 5x + 8
\]

Thus, the correct answer is:
D. \(x^{11}+10x^9+7x^8+6x^7+3x^3+5x+8\)
D
llama3.1-70B-Instruct

The correct answer is D.
D
llama3.1-405B-Instruct

D.
D
DeepSeek-Coder-V2 D D
Qwen2-72B-Instruct D. x^{11}+10x^9+7x^8+6x^7+3x^3+5x+8 D
baichuan4 D D
doubao D

$(9x^9+7x^8+4x^7)+(x^{11}+x^9+2x^7+3x^3+5x+8)$
$=x^{11}+(9x^9+x^9)+7x^8+(4x^7+2x^7)+3x^3+5x+8$
$=x^{11}+10x^9+7x^8+6x^7+3x^3+5x+8$.
D
minimax To simplify the expression, we need to combine like terms. The like terms are those that have the same degree of x. Let's combine the terms from both polynomials:

$(9x^9 + 7x^8 + 4x^7) + (x^{11} + x^9 + 2x^7 + 3x^3 + 5x + 8)$

Now, let's combine the like terms:

- There is only one $x^{11}$ term, so it remains as $x^{11}$.
- For $x^9$, we have $9x^9 + x^9 = 10x^9$.
- For $x^8$, we have $7x^8$ (no like terms to combine with).
- For $x^7$, we have $4x^7 + 2x^7 = 6x^7$.
- For $x^3$, we have $3x^3$ (no like terms to combine with).
- For $x$, we have $5x$ (no like terms to combine with).
- For the constant term, we have $8$ (no like terms to combine with).

So the simplified expression is:

$x^{11} + 10x^9 + 7x^8 + 6x^7 + 3x^3 + 5x + 8$

The correct answer is:

D. $x^{11} + 10x^9 + 7x^8 + 6x^7 + 3x^3 + 5x + 8$
D
kimi To simplify the given expression, we combine like terms:

\[
(9x^9 + 7x^8 + 4x^7) + (x^{11} + x^9 + 2x^7 + 3x^3 + 5x + 8)
\]

Combining the like terms:

\[
x^{11} + (9x^9 + x^9) + (7x^8) + (4x^7 + 2x^7) + 3x^3 + 5x + 8
\]

\[
= x^{11} + 10x^9 + 7x^8 + 6x^7 + 3x^3 + 5x + 8
\]

So the correct answer is:

D. \( x^{11}+10x^9+7x^8+6x^7+3x^3+5x+8 \)
D
wenxinyiyan D D
zhipu To simplify the given expression \((9x^9 + 7x^8 + 4x^7) + (x^{11} + x^9 + 2x^7 + 3x^3 + 5x + 8)\), we need to combine like terms.

Let's break it down step-by-step:

1. **Combine \(x^{11}\) terms:**
- There is only one \(x^{11}\) term: \(x^{11}\).

2. **Combine \(x^9\) terms:**
- From the first part: \(9x^9\)
- From the second part: \(x^9\)
- Combined: \(9x^9 + x^9 = 10x^9\)

3. **Combine \(x^8\) terms:**
- From the first part: \(7x^8\)
- From the second part: there is no \(x^8\) term.
- Combined: \(7x^8\)

4. **Combine \(x^7\) terms:**
- From the first part: \(4x^7\)
- From the second part: \(2x^7\)
- Combined: \(4x^7 + 2x^7 = 6x^7\)

5. **Combine \(x^3\) terms:**
- From the first part: there is no \(x^3\) term.
- From the second part: \(3x^3\)
- Combined: \(3x^3\)

6. **Combine \(x\) terms:**
- From the first part: there is no \(x\) term.
- From the second part: \(5x\)
- Combined: \(5x\)

7. **Combine constant terms:**
- From the first part: there is no constant term.
- From the second part: \(8\)
- Combined: \(8\)

Putting it all together, the simplified polynomial is:
\[ x^{11} + 10x^9 + 7x^8 + 6x^7 + 3x^3 + 5x + 8 \]

So, the correct answer is:
D. \( x^{11} + 10x^9 + 7x^8 + 6x^7 + 3x^3 + 5x + 8 \)

Answer: D
D
gpto1 D D
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