2018 · Q8
HCF and LCM of two polynomials are (x + 3) and (x³ — 9x² — x + 105) respectively. If one of the two polynomials is x² - 4x - 21, then the other is
Elementary MathematicsHCF and LCM
- Ax2x^2
- Bx2x^2
- Cx2−2x−15x^{2}-2x-15
- Dx2−x−15x^{2}-x-15
Explanation
The other polynomial = (HCF x LCM) / given polynomial = (x+3)(x^3 - 9x^2 - x + 105) / (x^2 - 4x - 21). Since x^2 - 4x - 21 = (x - 7)(x + 3), the (x + 3) factor cancels. Dividing x^3 - 9x^2 - x + 105 by (x - 7) gives x^2 - 2x - 15. Hence option C.