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degree 5 pol, p(x) + 1 is divisible by (x-1)^3, p(x)-1 divisible by (x+1)^3

Source: 1981 Swedish Mathematical Competition p3

March 28, 2021

polynomialdivisiblealgebra

Problem Statement

Find all polynomials

p(x)

of degree

5

such that

p(x) + 1

is divisible by

(x-1)^3

and

p(x) - 1

is divisible by

(x+1)^3