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Poland - Second Round
1963 Poland - Second Round
5
5
Part of
1963 Poland - Second Round
Problems
(1)
P(x) = nx^{n+2} -(n + 2)x^{n+1} + (n + 2)x-n is divisible (x - 1)^3
Source: Polish MO Second Round 1963 p5
8/31/2024
Prove that the polynomial
P
(
x
)
=
n
x
n
+
2
−
(
n
+
2
)
x
n
+
1
+
(
n
+
2
)
x
−
n
P(x) = nx^{n+2} -(n + 2)x^{n+1} + (n + 2)x-n
P
(
x
)
=
n
x
n
+
2
−
(
n
+
2
)
x
n
+
1
+
(
n
+
2
)
x
−
n
is divisible by the polynomial
(
x
−
1
)
3
(x - 1)^3
(
x
−
1
)
3
.
algebra
polynomial