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Mathematics
Problem
The polynomial
s
(
x
)
=
x
3
−
2
a
x
2
+
b
x
+
6
s(x)=x^{3}-2ax^{2}+bx+6
s
(
x
)
=
x
3
−
2
a
x
2
+
b
x
+
6
is exactly divisible by each of
(
x
−
1
)
(x-1)
(
x
−
1
)
and
(
x
+
2
)
(x+2)
(
x
+
2
)
. Find the corresponding values of
a
a
a
and
b
b
b
.
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