2012 · Q61
If p(x) is a common multiple of degree 6 of the polynomials f(x) = x^3 + x^2 - x - 1 and g(x) = x^3 - x^2 + x - 1 then which one of the following is correct?
Elementary MathematicsAlgebra
- Ap(x) = (x-1)^2 (x+1)^2 (x^2+1)
- Bp(x) = (x-1)(x+1)(x^2+1)^2
- Cp(x) = (x-1)^3 (x+1)(x^2+1)
- Dp(x) = (x-1)^2 (x^4+1)
Explanation
f = (x-1)(x+1)^2 and g = (x-1)(x^2+1); only (x-1)^2(x+1)^2(x^2+1) is a degree-6 polynomial divisible by both.