2026 · Q8
Which of the following expressions can divide both the polynomials x^3 + 2x^2 - 5x + 2 and x^3 + 4x^2 + x - 6 exactly?
- Ix - 1
- IIx + 1
- IIIx + 2
Select the correct answer using the code given below:
Elementary MathematicsHCF and LCM
- AI and II only
- BII and III only
- CI and III only
- DI only
Explanation
By the factor theorem, (x−a) divides a polynomial iff the value at a is zero. At x=1 both polynomials vanish (1+2−5+2=0 and 1+4+1−6=0), so x−1 divides both and statement I is correct. At x=−1 the first polynomial equals 8≠0, so x+1 fails; at x=−2 it equals 12≠0, so x+2 fails. Only I is correct, option D.