If 9x\(^2\) + 6xy + 4y\(^2\) is a factor of 27x\(^3\) - 8y\(^3\), find the other factor.
A
2y + 3x
B
2y - 3x
C
3x + 2y
D
3x - 2y
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Given that \( 9x^2 + 6xy + 4y^2 \) is a factor of \( 27x^3 - 8y^3 \), we can express:
\(27x^3 - 8y^3 = (3x - 2y)(9x^2 + 6xy + 4y^2)\)
Thus, the other factor is: 3x - 2y
Source: WAEC / JAMB / NECO Classroom Archive (Record #29566)