If the centroid of the triangle formed by the points (p, q), (q, r), and (r, p) is located at the origin (0, 0), what is the value of p³ + q³ + r³?

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A pqr
B 0
C p + q + r
D 3pqr

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Answer: D. 3pqr

Answer: D) 3pqr
Explanation: The x-coordinate of the centroid is (p + q + r)/3 = 0, so p + q + r = 0.
By the standard identity, if p + q + r = 0 then p³ + q³ + r³ = 3pqr.

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If the centroid of the triangle formed by the points (p, q), (q, r), and (r, p) is located at the origin (0, 0), what is the value of p³ + q³ + r³?

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