Question

question 5
which of the following is a factor of (f^2 + 4f + 3)?

• ((f + 1))
• ((f + 4))
• ((f - 3))
• ((f - 1))

question 6
which of the following is a factor of (x^2 - 8x + 15)?

• ((x - 3))
• ((x + 5))
• ((x + 3))
• ((x - 15))

question 7
one of the factors of (x^2 - 4x - 12) is

• ((x + 6))
• ((x - 3))
• ((x - 6))
• ((x + 12))

question 8
factor: (2k^2 + 8k + 8)

• ((2k - 4)(k - 2))
• (2(k - 2)(k + 2))
• ((2 - 2k)(k - 4))
• (2(k + 2)^2)

Explanation:

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"quick"
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"concepts_used": [
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"Greatest Common Factor"
],
"new_concepts": [],
"current_concepts": [
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"Greatest Common Factor"
]
}
</pre_analysis>

<reasoning>

Factor the trinomial in Question 5

\[

$$\begin{aligned} &f^2 + 4f + 3 = (f + 3)(f + 1) \end{aligned}$$

\]

Factor the trinomial in Question 6

\[

$$\begin{aligned} &x^2 - 8x + 15 = (x - 3)(x - 5) \end{aligned}$$

\]

Factor the trinomial in Question 7

\[

$$\begin{aligned} &x^2 - 4x - 12 = (x - 6)(x + 2) \end{aligned}$$

\]

Factor the expression in Question 8

\[

$$\begin{aligned} &2k^2 + 8k + 8 = 2(k^2 + 4k + 4) = 2(k + 2)^2 \end{aligned}$$

\]
</reasoning>

<answer>

Question 5

<mcq-correct>(A) \((f + 1)\)</mcq-correct>
<mcq-option>(B) \((f + 4)\)</mcq-option>
<mcq-option>(C) \((f - 3)\)</mcq-option>
<mcq-option>(D) \((f - 1)\)</mcq-option>

Question 6

<mcq-correct>(A) \((x - 3)\)</mcq-correct>
<mcq-option>(B) \((x + 5)\)</mcq-option>
<mcq-option>(C) \((x + 3)\)</mcq-option>
<mcq-option>(D) \((x - 15)\)</mcq-option>

Question 7

<mcq-option>(A) \((x + 6)\)</mcq-option>
<mcq-option>(B) \((x - 3)\)</mcq-option>
<mcq-correct>(C) \((x - 6)\)</mcq-correct>
<mcq-option>(D) \((x + 12)\)</mcq-option>

Question 8

<mcq-option>(A) \((2k - 4)(k - 2)\)</mcq-option>
<mcq-option>(B) \(2(k - 2)(k + 2)\)</mcq-option>
<mcq-option>(C) \((2 - 2k)(k - 4)\)</mcq-option>
<mcq-correct>(D) \(2(k + 2)^2\)</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Factoring Trinomials"
]
}
</post_analysis>

Answer:

<pre_analysis>
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"question_count": 4,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
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"needs_drawing": false,
"concepts_used": [
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"Greatest Common Factor"
],
"new_concepts": [],
"current_concepts": [
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"Greatest Common Factor"
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}
</pre_analysis>

<reasoning>

Factor the trinomial in Question 5

\[

$$\begin{aligned} &f^2 + 4f + 3 = (f + 3)(f + 1) \end{aligned}$$

\]

Factor the trinomial in Question 6

\[

$$\begin{aligned} &x^2 - 8x + 15 = (x - 3)(x - 5) \end{aligned}$$

\]

Factor the trinomial in Question 7

\[

$$\begin{aligned} &x^2 - 4x - 12 = (x - 6)(x + 2) \end{aligned}$$

\]

Factor the expression in Question 8

\[

$$\begin{aligned} &2k^2 + 8k + 8 = 2(k^2 + 4k + 4) = 2(k + 2)^2 \end{aligned}$$

\]
</reasoning>

<answer>

Question 5

<mcq-correct>(A) \((f + 1)\)</mcq-correct>
<mcq-option>(B) \((f + 4)\)</mcq-option>
<mcq-option>(C) \((f - 3)\)</mcq-option>
<mcq-option>(D) \((f - 1)\)</mcq-option>

Question 6

<mcq-correct>(A) \((x - 3)\)</mcq-correct>
<mcq-option>(B) \((x + 5)\)</mcq-option>
<mcq-option>(C) \((x + 3)\)</mcq-option>
<mcq-option>(D) \((x - 15)\)</mcq-option>

Question 7

<mcq-option>(A) \((x + 6)\)</mcq-option>
<mcq-option>(B) \((x - 3)\)</mcq-option>
<mcq-correct>(C) \((x - 6)\)</mcq-correct>
<mcq-option>(D) \((x + 12)\)</mcq-option>

Question 8

<mcq-option>(A) \((2k - 4)(k - 2)\)</mcq-option>
<mcq-option>(B) \(2(k - 2)(k + 2)\)</mcq-option>
<mcq-option>(C) \((2 - 2k)(k - 4)\)</mcq-option>
<mcq-correct>(D) \(2(k + 2)^2\)</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Factoring Trinomials"
]
}
</post_analysis>