Question

question 8
subtract the following polynomials: \\((5x^2 - 3x + 2) - (3x^2 + 9x - 11)\\)

• \\(2x^2 + 6x - 9\\)
• \\(2x^2 - 12x - 9\\)
• \\(2x^2 - 12x + 13\\)
• \\(8x^2 + 6x - 9\\)

question 9
subtract the following polynomials: \\((x^2 - 4) - (x^2 + 4)\\)

• \\(1\\)
• \\(-8\\)
• \\(0\\)
• \\(8\\)

Explanation:

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</pre_analysis>

<reasoning>

Distribute the negative sign for Question 8

\[
(5x^2 - 3x + 2) - (3x^2 + 9x - 11) = 5x^2 - 3x + 2 - 3x^2 - 9x + 11
\]

Combine like terms for Question 8

\[
(5x^2 - 3x^2) + (-3x - 9x) + (2 + 11) = 2x^2 - 12x + 13
\]

Simplify the expression for Question 9

\[
(x^2 - 4) - (x^2 + 4) = x^2 - 4 - x^2 - 4 = -8
\]
</reasoning>

<answer>

Question 8

<mcq-option>(A) \(2x^2 + 6x - 9\)</mcq-option>
<mcq-option>(B) \(2x^2 - 12x - 9\)</mcq-option>
<mcq-correct>(C) \(2x^2 - 12x + 13\)</mcq-correct>
<mcq-option>(D) \(8x^2 + 6x - 9\)</mcq-option>

Question 9

<mcq-option>(A) 1</mcq-option>
<mcq-correct>(B) -8</mcq-correct>
<mcq-option>(C) 0</mcq-option>
<mcq-option>(D) 8</mcq-option>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Polynomial Subtraction"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 2,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
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"concepts_used": [],
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],
"current_concepts": [
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"Combining Like Terms"
]
}
</pre_analysis>

<reasoning>

Distribute the negative sign for Question 8

\[
(5x^2 - 3x + 2) - (3x^2 + 9x - 11) = 5x^2 - 3x + 2 - 3x^2 - 9x + 11
\]

Combine like terms for Question 8

\[
(5x^2 - 3x^2) + (-3x - 9x) + (2 + 11) = 2x^2 - 12x + 13
\]

Simplify the expression for Question 9

\[
(x^2 - 4) - (x^2 + 4) = x^2 - 4 - x^2 - 4 = -8
\]
</reasoning>

<answer>

Question 8

<mcq-option>(A) \(2x^2 + 6x - 9\)</mcq-option>
<mcq-option>(B) \(2x^2 - 12x - 9\)</mcq-option>
<mcq-correct>(C) \(2x^2 - 12x + 13\)</mcq-correct>
<mcq-option>(D) \(8x^2 + 6x - 9\)</mcq-option>

Question 9

<mcq-option>(A) 1</mcq-option>
<mcq-correct>(B) -8</mcq-correct>
<mcq-option>(C) 0</mcq-option>
<mcq-option>(D) 8</mcq-option>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Polynomial Subtraction"
]
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</post_analysis>