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Mathematics
Problem
The polynomial
f
(
x
)
=
2
x
3
+
k
x
2
+
m
x
+
6
f(x)=2x^{3}+kx^{2}+mx+6
f
(
x
)
=
2
x
3
+
k
x
2
+
m
x
+
6
leaves a remainder of
4
4
4
when divided by
(
x
−
1
)
(x-1)
(
x
−
1
)
and a remainder of
−
2
-2
−
2
when divided by
(
x
+
2
)
(x+2)
(
x
+
2
)
. Which ordered pair
(
k
,
m
)
(k,m)
(
k
,
m
)
satisfies these conditions? a)
(
−
8
,
4
)
(-8,4)
(
−
8
,
4
)
b)
(
2
,
0
)
(2,0)
(
2
,
0
)
c)
(
0
,
−
4
)
(0,-4)
(
0
,
−
4
)
d)
(
4
,
−
8
)
(4,-8)
(
4
,
−
8
)
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