Question

7 factoriza cada expresión completamente.

\

$$\begin{tabular}{|c|c|} \\hline \\text{expresión} & \\text{forma factorizada} \\\\ \\hline 3 x^{2}-24 x & \\\\ \\hline 4 x^{2}-64 & \\\\ \\hline \\text{incógnita}^{2}-2 x-8 & \\\\ \\hline \\end{tabular}$$

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 3,
"skills_matched": [
"step_cot",
"table_formatter",
"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

\[
3x^2 - 24x = 3x(x - 8)
\]

Factorizar la segunda expresión

\[
4x^2 - 64 = 4(x^2 - 16) = 4(x - 4)(x + 4)
\]

Factorizar la tercera expresión

\[
x^2 - 2x - 8 = (x - 4)(x + 2)
\]
</reasoning>

<answer>

Expresión	Forma factorizada
\(4x^2 - 64\)	\(4(x - 4)(x + 4)\)
\(x^2 - 2x - 8\)	\((x - 4)(x + 2)\)

</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Trinomial Factoring"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 3,
"skills_matched": [
"step_cot",
"table_formatter",
"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

\[
3x^2 - 24x = 3x(x - 8)
\]

Factorizar la segunda expresión

\[
4x^2 - 64 = 4(x^2 - 16) = 4(x - 4)(x + 4)
\]

Factorizar la tercera expresión

\[
x^2 - 2x - 8 = (x - 4)(x + 2)
\]
</reasoning>

<answer>

Expresión	Forma factorizada
\(4x^2 - 64\)	\(4(x - 4)(x + 4)\)
\(x^2 - 2x - 8\)	\((x - 4)(x + 2)\)

</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Trinomial Factoring"
]
}
</post_analysis>