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Mathematics
Problem
A cubic polynomial is given by
p
(
x
)
=
2
x
3
+
a
x
2
+
b
x
+
c
p(x)=2x^3+ax^2+bx+c
p
(
x
)
=
2
x
3
+
a
x
2
+
b
x
+
c
. It satisfies the following conditions: (i)
(
x
−
1
)
(x-1)
(
x
−
1
)
is a factor of
p
(
x
)
p(x)
p
(
x
)
, (ii) the remainder obtained when
p
(
x
)
p(x)
p
(
x
)
is divided by
(
x
+
2
)
(x+2)
(
x
+
2
)
is
4
4
4
, and (iii)
p
(
0
)
=
3
p(0)=3
p
(
0
)
=
3
. Calculate the values of
a
a
a
,
b
b
b
and
c
c
c
.
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