Find a polynomial f(x) of degree 5 such that both of these properties hold:
* f(x) is divisible by x^3
* f(x) + 1 is divisible by (x + 1)(x + 2)(x + 3)
Write your answer in expanded form.
(x+1)(x+2)(x+3)
=(x^2+3x+2)(x+3)
=x^3+6x^2+11x+6
For the first one to be true, the lowest term is x^3, leaving only three possible terms. I don't think there is a solution to this equation.
