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Mathematics
Problem
The polynomial
p
(
x
)
=
2
x
3
+
a
x
2
+
b
x
−
12
p(x)=2x^{3}+ax^{2}+bx-12
p
(
x
)
=
2
x
3
+
a
x
2
+
b
x
−
12
leaves a remainder of
6
6
6
when divided by
x
−
1
x-1
x
−
1
and is exactly divisible by
x
+
2
x+2
x
+
2
. Which pair
(
a
,
b
)
(a,b)
(
a
,
b
)
satisfies these conditions? a)
a
=
9
,
b
=
8
a=9,\, b=8
a
=
9
,
b
=
8
b)
a
=
11
,
b
=
5
a=11,\, b=5
a
=
11
,
b
=
5
c)
a
=
10
,
b
=
6
a=10,\, b=6
a
=
10
,
b
=
6
d)
a
=
8
,
b
=
2
a=8,\, b=2
a
=
8
,
b
=
2
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