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Mathematics
Problem
Let
g
(
x
)
=
2
x
3
−
(
k
−
1
)
x
2
+
3
x
−
4
g(x)=2x^{3}-(k-1)x^{2}+3x-4
g
(
x
)
=
2
x
3
−
(
k
−
1
)
x
2
+
3
x
−
4
. (a) If the remainder when
g
(
x
)
g(x)
g
(
x
)
is divided by
x
−
2
x-2
x
−
2
is
10
10
10
, determine the value of
k
k
k
. (b) Using the value of
k
k
k
obtained in part (a), find the remainder when
g
(
x
)
g(x)
g
(
x
)
is divided by
x
+
1
x+1
x
+
1
.
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