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National and Regional Contests
Greece Contests
Greece National Olympiad
2014 Greece National Olympiad
1
Polynomials
Polynomials
Source:
February 22, 2014
algebra
polynomial
quadratics
Problem Statement
Find all the polynomials with real coefficients which satisfy
(
x
2
−
6
x
+
8
)
P
(
x
)
=
(
x
2
+
2
x
)
P
(
x
−
2
)
(x^2-6x+8)P(x)=(x^2+2x)P(x-2)
(
x
2
−
6
x
+
8
)
P
(
x
)
=
(
x
2
+
2
x
)
P
(
x
−
2
)
for all
x
∈
R
x\in \mathbb{R}
x
∈
R
.
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