QUESTION IMAGE
Question
7.)
\\(3x^2 - 24x\\)
\\(4x^2 - 64\\)
\\(x^2 - 2x - 8\\)
<pre_analysis>
{
"quality": "clear",
"question_count": 3,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Greatest Common Factor",
"Difference of Squares",
"Trinomial Factoring"
],
"new_concepts": [],
"current_concepts": [
"Greatest Common Factor",
"Difference of Squares",
"Trinomial Factoring"
]
}
</pre_analysis>
<reasoning>
Factorizar la primera expresión mediante factor común
\[
3x^2 - 24x = 3x(x - 8)
\]
Factorizar la segunda expresión mediante diferencia de cuadrados
\[
4x^2 - 64 = 4(x^2 - 16) = 4(x - 4)(x + 4)
\]
Factorizar el trinomio de la tercera expresión
\[
x^2 - 2x - 8 = (x - 4)(x + 2)
\]
</reasoning>
<answer>
Question 1
\[3x(x - 8)\]
Question 2
\[4(x - 4)(x + 4)\]
Question 3
\[(x - 4)(x + 2)\]
</answer>
<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Trinomial Factoring"
]
}
</post_analysis>
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<pre_analysis>
{
"quality": "clear",
"question_count": 3,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Greatest Common Factor",
"Difference of Squares",
"Trinomial Factoring"
],
"new_concepts": [],
"current_concepts": [
"Greatest Common Factor",
"Difference of Squares",
"Trinomial Factoring"
]
}
</pre_analysis>
<reasoning>
Factorizar la primera expresión mediante factor común
\[
3x^2 - 24x = 3x(x - 8)
\]
Factorizar la segunda expresión mediante diferencia de cuadrados
\[
4x^2 - 64 = 4(x^2 - 16) = 4(x - 4)(x + 4)
\]
Factorizar el trinomio de la tercera expresión
\[
x^2 - 2x - 8 = (x - 4)(x + 2)
\]
</reasoning>
<answer>
Question 1
\[3x(x - 8)\]
Question 2
\[4(x - 4)(x + 4)\]
Question 3
\[(x - 4)(x + 2)\]
</answer>
<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Trinomial Factoring"
]
}
</post_analysis>