Question on Polynomial.. ..
prove that x^n + a^n = 0 is the factor of (x-a)
Answers
Answered by
0
Step-by-step explanation:
According to factor theorem, if
x
−
k
is a factor of a polynomial function
f
(
x
)
, then
f
(
k
)
=
0
Now to test for
x
+
a
being a factor of
f
(
x
)
=
x
n
+
a
n
,
as
x
+
a
=
x
−
(
−
a
)
, we must check for
f
(
−
a
)
Now
f
(
x
)
=
x
n
+
a
n
Hence,
f
(
−
a
)
=
(
−
a
)
n
+
a
n
Observe if
n
is even then
f
(
−
a
)
=
(
−
a
)
n
+
a
n
=
a
n
+
a
n
=
2
a
n
≠
0
and hence
x
+
a
is not a factor of
x
n
+
a
n
if
n
is even
but if
n
is odd then
f
(
−
a
)
=
(
−
a
)
n
+
a
n
=
−
a
n
+
a
n
=
0
and hence
x+a
is a factor of
x^n + a^n
Similar questions
Social Sciences,
6 months ago
Computer Science,
6 months ago
Chemistry,
6 months ago
Biology,
1 year ago
English,
1 year ago
English,
1 year ago