4x^{3}+12x^{2}-x-3 is divisible by
- A. (2x+1) <strong>ONLY</strong>
- B. (2x-1) <strong>ONLY</strong>
- C. <strong>BOTH</strong> (2x+1) and (2x-1) ✓
- D. <strong>NEITHER</strong> (2x+1) <strong>NOR</strong> (2x-1)
Correct Answer: C. <strong>BOTH</strong> (2x+1) and (2x-1)
Explanation
Factorizing by grouping: 4x^2(x+3) - 1(x+3) = (4x^2-1)(x+3). Expanding 4x^2-1 gives (2x-1)(2x+1)(x+3). Therefore, the polynomial is divisible by both (2x+1) and (2x-1).
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