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Mathematics
Problem
Let
p
(
x
)
=
2
x
3
+
a
x
2
+
b
x
+
6
p(x)=2x^{3}+ax^{2}+bx+6
p
(
x
)
=
2
x
3
+
a
x
2
+
b
x
+
6
. Given that
(
x
−
1
)
(x-1)
(
x
−
1
)
is a factor of
p
(
x
)
p(x)
p
(
x
)
and that the remainder obtained on dividing
p
(
x
)
p(x)
p
(
x
)
by
(
x
+
2
)
(x+2)
(
x
+
2
)
is
20
20
20
, find the ordered pair
(
a
,
b
)
(a,b)
(
a
,
b
)
. a)
(
7
,
−
15
)
(7,-15)
(
7
,
−
15
)
b)
(
−
1
,
−
7
)
(-1,-7)
(
−
1
,
−
7
)
c)
(
7
3
,
−
31
3
)
\left(\dfrac{7}{3},-\dfrac{31}{3}\right)
(
3
7
,
−
3
31
)
d)
(
8
3
,
−
29
3
)
\left(\dfrac{8}{3},-\dfrac{29}{3}\right)
(
3
8
,
−
3
29
)
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