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10
2014 Algebra #10
2014 Algebra #10
Source:
July 8, 2022
2014
Algebra Test
Problem Statement
Let
p
(
x
)
=
c
1
+
c
2
⋅
2
x
+
c
3
⋅
3
x
+
c
4
⋅
5
x
+
c
5
⋅
8
x
p(x)=c_1+c_2\cdot2^x+c_3\cdot3^x+c_4\cdot5^x+c_5\cdot8^x
p
(
x
)
=
c
1
+
c
2
⋅
2
x
+
c
3
⋅
3
x
+
c
4
⋅
5
x
+
c
5
⋅
8
x
. Given that
p
(
k
)
=
k
p(k)=k
p
(
k
)
=
k
for
k
=
1
,
2
,
3
,
4
,
5
k=1,2,3,4,5
k
=
1
,
2
,
3
,
4
,
5
, compute
p
(
6
)
p(6)
p
(
6
)
.
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