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Mathematics
Mathematics
Problem
A polynomial in
x
x
x
of degree greater than three, leaves remainders 2, 1 and
−
1
-1
−
1
when divided, respectively, by
(
x
−
1
)
(x-1)
(
x
−
1
)
,
(
x
+
2
)
(x+2)
(
x
+
2
)
and
(
x
+
1
)
(x+1)
(
x
+
1
)
. What will be the remainder when it is divided by
(
x
−
1
)
(
x
+
2
)
(
x
+
1
)
(x-1)(x+2)(x+1)
(
x
−
1
)
(
x
+
2
)
(
x
+
1
)
.
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