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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
2
x
4
+
k
x
3
+
m
x
2
+
n
x
−
8
f(x)=2x^{4}+kx^{3}+mx^{2}+nx-8
f
(
x
)
=
2
x
4
+
k
x
3
+
m
x
2
+
n
x
−
8
. Given that
x
=
1
x=1
x
=
1
and
x
=
2
x=2
x
=
2
are factors of
f
(
x
)
f(x)
f
(
x
)
and that the remainder when
f
(
x
)
f(x)
f
(
x
)
is divided by
x
+
3
x+3
x
+
3
is
40
40
40
, determine the value of
k
k
k
. a)
2
2
2
b)
−
2
-2
−
2
c)
4
4
4
d)
−
4
-4
−
4
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