Question

solve for (m):
(m^2 - 27m = 0)

a. 0, 27
b. 0, -27
c. 27
d. 0

Explanation:

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<reasoning>

Rewrite the equation in standard form

Using the Quadratic Equations knowledge point
\[
m^2 - 27m = 0
\]

Factor out the greatest common factor

Using the Quadratic Equations knowledge point
\[
m(m - 27) = 0
\]

Set each factor to zero and solve

Using the Quadratic Equations knowledge point
\[

$$\begin{aligned} m = 0 \quad &\text{or} \quad m - 27 = 0 \\ m = 0 \quad &\text{or} \quad m = 27 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(a) 0, 27</mcq-correct>
<mcq-option>(b) 0, -27</mcq-option>
<mcq-option>(c) 27</mcq-option>
<mcq-option>(d) 0</mcq-option>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Quadratic Equations"
]
}
</post_analysis>

Answer:

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<reasoning>

Rewrite the equation in standard form

Using the Quadratic Equations knowledge point
\[
m^2 - 27m = 0
\]

Factor out the greatest common factor

Using the Quadratic Equations knowledge point
\[
m(m - 27) = 0
\]

Set each factor to zero and solve

Using the Quadratic Equations knowledge point
\[

$$\begin{aligned} m = 0 \quad &\text{or} \quad m - 27 = 0 \\ m = 0 \quad &\text{or} \quad m = 27 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(a) 0, 27</mcq-correct>
<mcq-option>(b) 0, -27</mcq-option>
<mcq-option>(c) 27</mcq-option>
<mcq-option>(d) 0</mcq-option>
</answer>

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"knowledge_point": [
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