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Mathematics
Mathematics
Problem
The polynomial
f
(
x
)
f(x)
f
(
x
)
leaves the same remainder when divided by
(
x
−
1
)
(x-1)
(
x
−
1
)
and
(
x
+
1
)
(x+1)
(
x
+
1
)
. Which of the following must hold? a)
(
x
−
1
)
(
x
+
1
)
(x-1)(x+1)
(
x
−
1
)
(
x
+
1
)
is a factor of
f
(
x
)
f(x)
f
(
x
)
b)
f
(
1
)
+
f
(
−
1
)
=
0
f(1)+f(-1)=0
f
(
1
)
+
f
(
−
1
)
=
0
c)
f
(
1
)
=
f
(
−
1
)
f(1)=f(-1)
f
(
1
)
=
f
(
−
1
)
d) The degree of
f
(
x
)
f(x)
f
(
x
)
is even
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