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Mathematics
Problem
A polynomial
p
(
x
)
=
a
x
2
+
b
x
+
6
p(x)=ax^{2}+bx+6
p
(
x
)
=
a
x
2
+
b
x
+
6
leaves a remainder
4
4
4
when divided by
(
x
−
1
)
(x-1)
(
x
−
1
)
and a remainder
−
6
-6
−
6
when divided by
(
x
+
2
)
(x+2)
(
x
+
2
)
. Which ordered pair
(
a
,
b
)
(a,b)
(
a
,
b
)
satisfies these conditions? a)
(
−
5
3
,
−
1
3
)
\left(-\dfrac{5}{3},-\dfrac{1}{3}\right)
(
−
3
5
,
−
3
1
)
b)
(
−
4
,
2
)
(-4,2)
(
−
4
,
2
)
c)
(
−
8
3
,
2
3
)
\left(-\dfrac{8}{3},\dfrac{2}{3}\right)
(
−
3
8
,
3
2
)
d)
(
−
4
,
−
2
)
(-4,-2)
(
−
4
,
−
2
)
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