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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.

 Apr 5, 2023
 #1
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(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.

 May 3, 2023

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