Teaching NVS TGT 2024 Test Series Quantitative Aptitude Algebra Polynomials

The HCF of two polynomials p(x) and q(x) is 2x(x + 2) and LCM is 24x(x + 2)2(x - 2). If p(x)=8x3 + 32x2 + 32x, then what is q(x) equal to?

1
4x3 - 16x
2
6x3 - 24x
3
12x3 + 24x
4
12x3 - 24x
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