Question

if \\(x - 9\\) is a factor of \\(x^2 - 5x - 36\\), what is the other factor?

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

Explanation:

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<reasoning>

Identify the given polynomial and known factor

\[

$$\begin{aligned} P(x) &= x^2 - 5x - 36 \\ F_1(x) &= x - 9 \end{aligned}$$

\]

Find the other factor by division or factoring

\[

$$\begin{aligned} x^2 - 5x - 36 &= (x - 9)(x + a) \\ -9 \cdot a &= -36 \implies a = 4 \\ x^2 - 5x - 36 &= (x - 9)(x + 4) \end{aligned}$$

\]

Select the matching option

\[
F_2(x) = x + 4
\]
</reasoning>

<answer>
<mcq-option>\(x - 4\)</mcq-option>
<mcq-correct>\(x + 4\)</mcq-correct>
<mcq-option>\(x - 6\)</mcq-option>
<mcq-option>\(x + 6\)</mcq-option>
</answer>

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

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</pre_analysis>

<reasoning>

Identify the given polynomial and known factor

\[

$$\begin{aligned} P(x) &= x^2 - 5x - 36 \\ F_1(x) &= x - 9 \end{aligned}$$

\]

Find the other factor by division or factoring

\[

$$\begin{aligned} x^2 - 5x - 36 &= (x - 9)(x + a) \\ -9 \cdot a &= -36 \implies a = 4 \\ x^2 - 5x - 36 &= (x - 9)(x + 4) \end{aligned}$$

\]

Select the matching option

\[
F_2(x) = x + 4
\]
</reasoning>

<answer>
<mcq-option>\(x - 4\)</mcq-option>
<mcq-correct>\(x + 4\)</mcq-correct>
<mcq-option>\(x - 6\)</mcq-option>
<mcq-option>\(x + 6\)</mcq-option>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
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