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40
Prove that f(x) is not divisible by x^2 - x + 1
Prove that f(x) is not divisible by x^2 - x + 1
Source:
January 28, 2011
algebra
polynomial
algebra unsolved
Problem Statement
Let
g
(
x
)
g(x)
g
(
x
)
be a fixed polynomial with real coefficients and define
f
(
x
)
f(x)
f
(
x
)
by
f
(
x
)
=
x
2
+
x
g
(
x
3
)
f(x) =x^2 + xg(x^3)
f
(
x
)
=
x
2
+
xg
(
x
3
)
. Show that
f
(
x
)
f(x)
f
(
x
)
is not divisible by
x
2
ā
x
+
1
x^2 - x + 1
x
2
ā
x
+
1
.
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