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12
Purple Comet 2017 HS problem 12
Purple Comet 2017 HS problem 12
Source:
March 19, 2020
polynomial
algebra
Problem Statement
Let
P
P
P
be a polynomial satisfying
P
(
x
+
1
)
+
P
(
x
ā
1
)
=
x
3
P(x + 1) + P(x - 1) = x^3
P
(
x
+
1
)
+
P
(
x
ā
1
)
=
x
3
for all real numbers
x
x
x
. Find the value of
P
(
12
)
P(12)
P
(
12
)
.
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