Question

juanita begins to factor an expression as shown.

(x^2+3x-18=(x+\square)(x-\square))

what numbers should be placed in the boxes from left to right?

3 and 6
2 and 9
6 and 3
9 and 2

Explanation:

<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",
"Trinomial Coefficients"
]
}
</pre_analysis>

<reasoning>

Identify the trinomial and target structure

\[
x^2 + 3x - 18 = (x + \square)(x - \square)
\]

Find factors of -18 that sum to 3

\[

$$\begin{aligned} &a \cdot (-b) = -18 \\ &a - b = 3 \\ &a = 6, \quad b = 3 \end{aligned}$$

\]

Match the values to the boxes

\[
(x + 6)(x - 3)
\]
The numbers in the boxes from left to right are 6 and 3.
</reasoning>

<answer>
<mcq-option>3 and 6</mcq-option>
<mcq-option>2 and 9</mcq-option>
<mcq-correct>6 and 3</mcq-correct>
<mcq-option>9 and 2</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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"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
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"concepts_used": [
"Factoring Trinomials"
],
"new_concepts": [],
"current_concepts": [
"Factoring Trinomials",
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]
}
</pre_analysis>

<reasoning>

Identify the trinomial and target structure

\[
x^2 + 3x - 18 = (x + \square)(x - \square)
\]

Find factors of -18 that sum to 3

\[

$$\begin{aligned} &a \cdot (-b) = -18 \\ &a - b = 3 \\ &a = 6, \quad b = 3 \end{aligned}$$

\]

Match the values to the boxes

\[
(x + 6)(x - 3)
\]
The numbers in the boxes from left to right are 6 and 3.
</reasoning>

<answer>
<mcq-option>3 and 6</mcq-option>
<mcq-option>2 and 9</mcq-option>
<mcq-correct>6 and 3</mcq-correct>
<mcq-option>9 and 2</mcq-option>
</answer>

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