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7.) \\(3x^2 - 24x\\) \\(4x^2 - 64\\) \\(x^2 - 2x - 8\\)

Question

7.)

\\(3x^2 - 24x\\)

\\(4x^2 - 64\\)

\\(x^2 - 2x - 8\\)

Explanation:

Response

<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>

Answer:

<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>