2023 · Q2
If (x − 1)³ is a factor of x⁴ + αx³ + βx² + γx − 1, then the other factor will be:
Elementary MathematicsAlgebra
- Ax + 1
- Bx − 3
- Cx + 2
- Dx
Explanation
Write x^4+alpha x^3+beta x^2+gamma x-1 = (x+a)(x-1)^3. Expanding (x+a)(x^3-3x^2+3x-1) gives constant term -a, which must equal -1, so a=1. The other factor is (x+1). Option (a).