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Problems
Contests
International Contests
Pan African
2000 Pan African
2
Polynomial
Polynomial
Source: Pan African 2000
October 3, 2005
algebra
polynomial
quadratics
Problem Statement
Define the polynomials
P
0
,
P
1
,
P
2
⋯
P_0, P_1, P_2 \cdots
P
0
,
P
1
,
P
2
⋯
by:
P
0
(
x
)
=
x
3
+
213
x
2
−
67
x
−
2000
P_0(x)=x^3+213x^2-67x-2000
P
0
(
x
)
=
x
3
+
213
x
2
−
67
x
−
2000
P
n
(
x
)
=
P
n
−
1
(
x
−
n
)
,
n
∈
N
P_n(x)=P_{n-1}(x-n), n \in N
P
n
(
x
)
=
P
n
−
1
(
x
−
n
)
,
n
∈
N
Find the coefficient of
x
x
x
in
P
21
(
x
)
P_{21}(x)
P
21
(
x
)
.
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