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Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2008 National Olympiad First Round
3
3
Part of
2008 National Olympiad First Round
Problems
(1)
Turkey NMO 2008 1st Round - P03 (Algebra)
Source:
8/24/2012
Let
P
(
x
)
=
1
−
x
+
x
2
−
x
3
+
⋯
+
x
18
−
x
19
P(x) = 1-x+x^2-x^3+\dots+x^{18}-x^{19}
P
(
x
)
=
1
−
x
+
x
2
−
x
3
+
⋯
+
x
18
−
x
19
and
Q
(
x
)
=
P
(
x
−
1
)
Q(x)=P(x-1)
Q
(
x
)
=
P
(
x
−
1
)
. What is the coefficient of
x
2
x^2
x
2
in polynomial
Q
Q
Q
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
840
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
816
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
969
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
1020
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
1140
<span class='latex-bold'>(A)</span>\ 840 \qquad<span class='latex-bold'>(B)</span>\ 816 \qquad<span class='latex-bold'>(C)</span>\ 969 \qquad<span class='latex-bold'>(D)</span>\ 1020 \qquad<span class='latex-bold'>(E)</span>\ 1140
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
840
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
816
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
969
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
1020
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
1140
algebra
polynomial