Question

2.) \\((8x^4 - 6x) - (7x^3 + 2x^2 - x)\\)

3.) \\((x + 6)(4x - 3)\\)

4.) \\((x - 7)^2 = 25\\)

6.) \\(x^2 - 5x - 36 = 0\\)

Explanation:

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"explain_then_answer",
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],
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"concepts_used": [
"Polynomial Subtraction",
"Polynomial Multiplication",
"Square Root Method",
"Solving Quadratics by Factoring"
],
"new_concepts": [],
"current_concepts": [
"Polynomial Subtraction",
"Polynomial Multiplication",
"Square Root Method",
"Solving Quadratics by Factoring"
]
}
</pre_analysis>

<reasoning>

Restar los polinomios en la pregunta 2

\[
(8x^4 - 6x) - (7x^3 + 2x^2 - x) = 8x^4 - 7x^3 - 2x^2 - 6x + x = 8x^4 - 7x^3 - 2x^2 - 5x
\]

Multiplicar los binomios en la pregunta 3

\[
(x + 6)(4x - 3) = 4x^2 - 3x + 24x - 18 = 4x^2 + 21x - 18
\]

Resolver las ecuaciones cuadráticas en las preguntas 4 y 6

\[

$$\begin{aligned} &\text{Pregunta 4: } (x - 7)^2 = 25 \implies x - 7 = \pm 5 \implies x = 12 \quad \text{o} \quad x = 2\\ &\text{Pregunta 6: } x^2 - 5x - 36 = 0 \implies (x - 9)(x + 4) = 0 \implies x = 9 \quad \text{o} \quad x = -4 \end{aligned}$$

\]
</reasoning>

<answer>

Question 2

\[8x^4 - 7x^3 - 2x^2 - 5x\]

Question 3

\[4x^2 + 21x - 18\]

Question 4

\[x = 12, \quad x = 2\]

Question 6

\[x = 9, \quad x = -4\]
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Algebra",
"Solving Quadratics by Factoring"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 4,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Polynomial Subtraction",
"Polynomial Multiplication",
"Square Root Method",
"Solving Quadratics by Factoring"
],
"new_concepts": [],
"current_concepts": [
"Polynomial Subtraction",
"Polynomial Multiplication",
"Square Root Method",
"Solving Quadratics by Factoring"
]
}
</pre_analysis>

<reasoning>

Restar los polinomios en la pregunta 2

\[
(8x^4 - 6x) - (7x^3 + 2x^2 - x) = 8x^4 - 7x^3 - 2x^2 - 6x + x = 8x^4 - 7x^3 - 2x^2 - 5x
\]

Multiplicar los binomios en la pregunta 3

\[
(x + 6)(4x - 3) = 4x^2 - 3x + 24x - 18 = 4x^2 + 21x - 18
\]

Resolver las ecuaciones cuadráticas en las preguntas 4 y 6

\[

$$\begin{aligned} &\text{Pregunta 4: } (x - 7)^2 = 25 \implies x - 7 = \pm 5 \implies x = 12 \quad \text{o} \quad x = 2\\ &\text{Pregunta 6: } x^2 - 5x - 36 = 0 \implies (x - 9)(x + 4) = 0 \implies x = 9 \quad \text{o} \quad x = -4 \end{aligned}$$

\]
</reasoning>

<answer>

Question 2

\[8x^4 - 7x^3 - 2x^2 - 5x\]

Question 3

\[4x^2 + 21x - 18\]

Question 4

\[x = 12, \quad x = 2\]

Question 6

\[x = 9, \quad x = -4\]
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Algebra",
"Solving Quadratics by Factoring"
]
}
</post_analysis>