Which of the following expressions can divide both the polynomials x^3 + 2x^2 - 5x + 2 and x^3 + 4x^2 + x - 6 exactly ? I. x - 1 II. x + 1 III. x + 2 Select the correct answer using the code given below :
- A. I and II only
- B. II and III only
- C. I and III only
- D. I only ✓
Correct Answer: D. I only
Explanation
By the Factor Theorem, substituting x=1 (from x-1=0) into both polynomials yields 0, confirming it's a factor. Checking x=-1 and x=-2 shows they do not give 0 for both polynomials.
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