x⁵-5x³+4x..(factorise)
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Algebra Examples
Popular Problems Algebra Solve by Factoring x^5-5x^3+4x=0
x
5
−
5
x
3
+
4
x
=
0
Factor
x
out of
x
5
−
5
x
3
+
4
x
.
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x
(
x
4
−
5
x
2
+
4
)
=
0
Rewrite
x
4
as
(
x
2
)
2
.
x
(
(
x
2
)
2
−
5
x
2
+
4
)
=
0
Let
u
=
x
2
. Substitute
u
for all occurrences of
x
2
.
x
(
u
2
−
5
u
+
4
)
=
0
Factor
u
2
−
5
u
+
4
using the AC method.
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x
(
(
u
−
4
)
(
u
−
1
)
)
=
0
Replace all occurrences of
u
with
x
2
.
x
(
(
x
2
−
4
)
(
x
2
−
1
)
)
=
0
Rewrite
4
as
2
2
.
x
(
(
x
2
−
2
2
)
(
x
2
−
1
)
)
=
0
Since both terms are perfect squares, factor using the difference of squares formula,
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
where
a
=
x
and
b
=
2
.
x
(
(
x
+
2
)
(
x
−
2
)
(
x
2
−
1
)
)
=
0
Rewrite
1
as
1
2
.
x
(
(
x
+
2
)
(
x
−
2
)
(
x
2
−
1
2
)
)
=
0
Factor.
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x
(
x
+
2
)
(
x
−
2
)
(
x
+
1
)
(
x
−
1
)
=
0
If any individual factor on the left side of the equation is equal to
0
, the entire expression will be equal to
0
.
x
=
0
x
+
2
=
0
x
−
2
=
0
x
+
1
=
0
x
−
1
=
0
Set the first factor equal to
0
.
x
=
0
Set the next factor equal to
0
and solve.
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x
=
−
2
Set the next factor equal to
0
and solve.
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x
=
2
Set the next factor equal to
0
and solve.
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x
=
−
1
Set the next factor equal to
0
and solve.
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x
=
1
The final solution is all the values that make
x
(
x
+
2
)
(
x
−
2
)
(
x
+
1
)
(
x
−
1
)
=
0
true.
x
=
0
,
−
2
,
2
,
−
1
,
1