Question

question 1
evaluate the polynomial \\(3x^2 - 2x + 5\\) when \\(x = 4\\)

question 2
evaluate the polynomial \\(x^3 + 2x^2 - 8x - 2\\) when \\(x = -2\\)

question 3
combine like terms: \\(4x^3 + 9x^3\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 3,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Polynomial Evaluation",
"Combining Like Terms"
],
"current_concepts": [
"Polynomial Evaluation",
"Combining Like Terms"
]
}
</pre_analysis>

<reasoning>

Evaluate the first polynomial

\[

$$\begin{aligned} &P(x) = 3x^2 - 2x + 5,\quad x = 4\\ &P(4) = 3(4)^2 - 2(4) + 5\\ &P(4) = 3(16) - 8 + 5\\ &P(4) = 48 - 8 + 5 = 45 \end{aligned}$$

\]

Evaluate the second polynomial

\[

$$\begin{aligned} &Q(x) = x^3 + 2x^2 - 8x - 2,\quad x = -2\\ &Q(-2) = (-2)^3 + 2(-2)^2 - 8(-2) - 2\\ &Q(-2) = -8 + 2(4) + 16 - 2\\ &Q(-2) = -8 + 8 + 16 - 2 = 14 \end{aligned}$$

\]

Combine like terms

\[

$$\begin{aligned} &4x^3 + 9x^3\\ &(4 + 9)x^3 = 13x^3 \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

Evaluate the polynomial \(3x^2 - 2x + 5\) when \(x = 4\) <blank>45</blank>

Question 2

Evaluate the polynomial \(x^3 + 2x^2 - 8x - 2\) when \(x = -2\) <blank>14</blank>

Question 3

Combine like terms: \(4x^3 + 9x^3\) <blank>\(13x^3\)</blank>
</answer>

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

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 3,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Polynomial Evaluation",
"Combining Like Terms"
],
"current_concepts": [
"Polynomial Evaluation",
"Combining Like Terms"
]
}
</pre_analysis>

<reasoning>

Evaluate the first polynomial

\[

$$\begin{aligned} &P(x) = 3x^2 - 2x + 5,\quad x = 4\\ &P(4) = 3(4)^2 - 2(4) + 5\\ &P(4) = 3(16) - 8 + 5\\ &P(4) = 48 - 8 + 5 = 45 \end{aligned}$$

\]

Evaluate the second polynomial

\[

$$\begin{aligned} &Q(x) = x^3 + 2x^2 - 8x - 2,\quad x = -2\\ &Q(-2) = (-2)^3 + 2(-2)^2 - 8(-2) - 2\\ &Q(-2) = -8 + 2(4) + 16 - 2\\ &Q(-2) = -8 + 8 + 16 - 2 = 14 \end{aligned}$$

\]

Combine like terms

\[

$$\begin{aligned} &4x^3 + 9x^3\\ &(4 + 9)x^3 = 13x^3 \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

Evaluate the polynomial \(3x^2 - 2x + 5\) when \(x = 4\) <blank>45</blank>

Question 2

Evaluate the polynomial \(x^3 + 2x^2 - 8x - 2\) when \(x = -2\) <blank>14</blank>

Question 3

Combine like terms: \(4x^3 + 9x^3\) <blank>\(13x^3\)</blank>
</answer>

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