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Mathematics
Problem
The polynomial
f
(
x
)
=
3
x
3
+
2
k
x
2
+
5
x
−
8
f(x)=3x^{3}+2kx^{2}+5x-8
f
(
x
)
=
3
x
3
+
2
k
x
2
+
5
x
−
8
is such that the remainder obtained on division by
(
x
−
1
)
(x-1)
(
x
−
1
)
is twice the remainder obtained on division by
(
x
+
2
)
(x+2)
(
x
+
2
)
. Determine the value of
k
k
k
.
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