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Mathematics
Problem
Let
p
(
x
)
=
a
(
x
−
2
)
3
+
b
(
x
−
2
)
2
+
c
(
x
−
2
)
+
d
p(x)=a(x-2)^{3}+b(x-2)^{2}+c(x-2)+d
p
(
x
)
=
a
(
x
−
2
)
3
+
b
(
x
−
2
)
2
+
c
(
x
−
2
)
+
d
. Determine the coefficients
a
a
a
,
b
b
b
,
c
c
c
, and
d
d
d
so that
p
(
2
)
=
4
p(2)=4
p
(
2
)
=
4
,
p
′
(
2
)
=
0
p'(2)=0
p
′
(
2
)
=
0
,
p
′
′
(
2
)
=
−
3
p''(2)=-3
p
′′
(
2
)
=
−
3
, and
p
(
3
)
=
5
p(3)=5
p
(
3
)
=
5
.
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