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2012 CHMMC Spring
4
2012 Spring Team #4
2012 Spring Team #4
Source:
March 20, 2022
algebra
Problem Statement
Let
P
(
x
)
P(x)
P
(
x
)
be a monic polynomial of degree
3
3
3
. Suppose that
P
(
x
)
P(x)
P
(
x
)
has remainder
R
(
x
)
R(x)
R
(
x
)
when it is divided by
(
x
−
1
)
(
x
−
4
)
(x - 1)(x - 4)
(
x
−
1
)
(
x
−
4
)
and
2
R
(
x
)
2R(x)
2
R
(
x
)
when it is divided by
(
x
−
2
)
(
x
−
3
)
(x - 2)(x - 3)
(
x
−
2
)
(
x
−
3
)
. Given that
P
(
0
)
=
5
P(0) = 5
P
(
0
)
=
5
, find
P
(
5
)
P(5)
P
(
5
)
.
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