Question

the factorization of \\(x^2 + 3x - 4\\) is modeled with algebra tiles.

what are the factors of \\(x^2 + 3x - 4\\)?

(x + 4) and (x - 4)
(x + 3) and (x - 4)
(x + 4) and (x - 1)
(x + 3) and (x - 1)

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": [
"Algebra Tiles",
"Factoring Trinomials"
],
"new_concepts": [],
"current_concepts": [
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"Factoring Trinomials"
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}
</pre_analysis>

<reasoning>

Identify the quadratic expression and its components

\[
x^2 + 3x - 4
\]

Find two numbers that multiply to the constant term and add to the linear coefficient

\[

$$\begin{aligned} a \cdot b &= -4 \\ a + b &= 3 \\ \text{Thus, } a &= 4, \quad b = -1 \end{aligned}$$

\]

Write the factored form of the trinomial

\[
x^2 + 3x - 4 = (x + 4)(x - 1)
\]
</reasoning>

<answer>
<mcq-option>(x + 4) and (x - 4)</mcq-option>
<mcq-option>(x + 3) and (x - 4)</mcq-option>
<mcq-correct>(x + 4) and (x - 1)</mcq-correct>
<mcq-option>(x + 3) and (x - 1)</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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"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Algebra Tiles",
"Factoring Trinomials"
],
"new_concepts": [],
"current_concepts": [
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]
}
</pre_analysis>

<reasoning>

Identify the quadratic expression and its components

\[
x^2 + 3x - 4
\]

Find two numbers that multiply to the constant term and add to the linear coefficient

\[

$$\begin{aligned} a \cdot b &= -4 \\ a + b &= 3 \\ \text{Thus, } a &= 4, \quad b = -1 \end{aligned}$$

\]

Write the factored form of the trinomial

\[
x^2 + 3x - 4 = (x + 4)(x - 1)
\]
</reasoning>

<answer>
<mcq-option>(x + 4) and (x - 4)</mcq-option>
<mcq-option>(x + 3) and (x - 4)</mcq-option>
<mcq-correct>(x + 4) and (x - 1)</mcq-correct>
<mcq-option>(x + 3) and (x - 1)</mcq-option>
</answer>

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