Question

which expression has an equivalent value to \\(x^2 + 9x + 8\\) for all values of \\(x\\)?

\\((x + 1)(x + 8)\\)
\\((x + 2)(x + 6)\\)
\\((x + 4)(x + 4)\\)
\\((x + 5)(x + 4)\\)

Explanation:

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<reasoning>

Identify the quadratic expression

\[
x^2 + 9x + 8
\]

Find factors that multiply to 8 and add to 9

\[

$$\begin{aligned} &\text{Factors of 8: } 1 \times 8 = 8 \\ &\text{Sum of factors: } 1 + 8 = 9 \end{aligned}$$

\]

Write the factored form

\[
(x + 1)(x + 8)
\]
</reasoning>

<answer>
<mcq-correct>(x + 1)(x + 8)</mcq-correct>
<mcq-option>(x + 2)(x + 6)</mcq-option>
<mcq-option>(x + 4)(x + 4)</mcq-option>
<mcq-option>(x + 5)(x + 4)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Factoring Trinomials"
]
}
</post_analysis>

Answer:

<pre_analysis>
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"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
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"concepts_used": [
"Factoring Trinomials"
],
"new_concepts": [],
"current_concepts": [
"Factoring Trinomials",
"Polynomial Multiplication"
]
}
</pre_analysis>

<reasoning>

Identify the quadratic expression

\[
x^2 + 9x + 8
\]

Find factors that multiply to 8 and add to 9

\[

$$\begin{aligned} &\text{Factors of 8: } 1 \times 8 = 8 \\ &\text{Sum of factors: } 1 + 8 = 9 \end{aligned}$$

\]

Write the factored form

\[
(x + 1)(x + 8)
\]
</reasoning>

<answer>
<mcq-correct>(x + 1)(x + 8)</mcq-correct>
<mcq-option>(x + 2)(x + 6)</mcq-option>
<mcq-option>(x + 4)(x + 4)</mcq-option>
<mcq-option>(x + 5)(x + 4)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Factoring Trinomials"
]
}
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