The HCF and LCM of two polynomials are 3x+1 and 30x^{3}+7x^{2}-10x-3 respectively. If one polynomial is 6x^{2}+5x+1, then what is the other polynomial?
- A. 15x^{2}+4x+3
- B. 15x^{2}+4x-3
- C. 15x^{2}-4x+3
- D. 15x^{2}-4x-3 ✓
Correct Answer: D. 15x^{2}-4x-3
Explanation
Using \text{LCM} \times \text{HCF} = P_1 \times P_2, we have P_2 = \frac{(3x+1)(30x^3+7x^2-10x-3)}{6x^2+5x+1}. Since 6x^2+5x+1 = (3x+1)(2x+1), dividing the numerator by (2x+1) yields 15x^2 - 4x - 3.
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