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Mathematics
Problem
Write
2
x
4
−
3
x
3
+
5
x
2
−
4
x
+
1
x
2
+
1
\dfrac{2x^{4}-3x^{3}+5x^{2}-4x+1}{x^{2}+1}
x
2
+
1
2
x
4
−
3
x
3
+
5
x
2
−
4
x
+
1
in the form
S
(
x
)
+
R
(
x
)
x
2
+
1
S(x)+\dfrac{R(x)}{x^{2}+1}
S
(
x
)
+
x
2
+
1
R
(
x
)
, where
deg
R
<
2
\deg R<2
de
g
R
<
2
. Which of the following is correct? a)
2
x
2
−
3
x
−
3
+
x
−
2
x
2
+
1
2x^{2}-3x-3+\dfrac{x-2}{x^{2}+1}
2
x
2
−
3
x
−
3
+
x
2
+
1
x
−
2
b)
2
x
2
−
3
x
−
x
+
2
x
2
+
1
2x^{2}-3x-\dfrac{x+2}{x^{2}+1}
2
x
2
−
3
x
−
x
2
+
1
x
+
2
c)
2
x
2
−
3
x
+
3
−
x
+
2
x
2
+
1
2x^{2}-3x+3-\dfrac{x+2}{x^{2}+1}
2
x
2
−
3
x
+
3
−
x
2
+
1
x
+
2
d)
2
x
2
−
3
x
+
3
+
x
+
2
x
2
+
1
2x^{2}-3x+3+\dfrac{x+2}{x^{2}+1}
2
x
2
−
3
x
+
3
+
x
2
+
1
x
+
2
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