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1986 AIME Problems
11
Polynomial Coefficients
Polynomial Coefficients
Source:
December 22, 2005
algebra
polynomial
ratio
binomial theorem
AIME
Problem Statement
The polynomial
1
−
x
+
x
2
−
x
3
+
⋯
+
x
16
−
x
17
1-x+x^2-x^3+\cdots+x^{16}-x^{17}
1
−
x
+
x
2
−
x
3
+
⋯
+
x
16
−
x
17
may be written in the form
a
0
+
a
1
y
+
a
2
y
2
+
⋯
+
a
16
y
16
+
a
17
y
17
a_0+a_1y+a_2y^2+\cdots +a_{16}y^{16}+a_{17}y^{17}
a
0
+
a
1
y
+
a
2
y
2
+
⋯
+
a
16
y
16
+
a
17
y
17
, where
y
=
x
+
1
y=x+1
y
=
x
+
1
and thet
a
i
a_i
a
i
's are constants. Find the value of
a
2
a_2
a
2
.
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