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Mathematics
Problem
A polynomial
p
(
x
)
=
2
x
3
−
x
2
+
x
−
1
p(x)=2x^{3}-x^{2}+x-1
p
(
x
)
=
2
x
3
−
x
2
+
x
−
1
is divided by a polynomial
g
(
x
)
g(x)
g
(
x
)
to give a quotient
q
(
x
)
=
2
x
−
3
q(x)=2x-3
q
(
x
)
=
2
x
−
3
and a remainder
r
(
x
)
=
5
r(x)=5
r
(
x
)
=
5
. Determine
g
(
x
)
g(x)
g
(
x
)
. a)
x
2
−
x
+
2
x^{2}-x+2
x
2
−
x
+
2
b)
2
x
2
−
3
x
+
5
2x^{2}-3x+5
2
x
2
−
3
x
+
5
c)
x
2
+
x
+
2
x^{2}+x+2
x
2
+
x
+
2
d)
x
2
+
x
−
2
x^{2}+x-2
x
2
+
x
−
2
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