x³-8x²+6+24 factorize
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Answer:
We can see that
x
is common to all the terms. We can write it as
x
⋅
(
x
2
−
8
x
+
15
)
Now we need to factorise
x
2
−
8
x
+
15
We can use Splitting the Middle Term technique to factorise this.
It is in the form
a
x
2
+
b
x
+
c
where
a
=
1
,
b
=
−
8
,
c
=
15
To split the middle term, we need to think of two numbers
N
1
and
N
2
such that:
N
1
⋅
N
2
=
a
⋅
c
and
N
1
+
N
2
=
b
N
1
⋅
N
2
=
(
1
)
⋅
(
15
)
and
N
1
+
N
2
=
−
8
N
1
⋅
N
2
=
15
and
N
1
+
N
2
=
−
8
After Trial and Error, we get
N
1
=
−
3
and
N
2
=
−
5
(
−
3
)
⋅
(
−
5
)
=
15
and
(
−
3
)
+
(
−
5
)
=
−
8
So we can write the expression
x
2
−
8
x
+
15
as
x
2
−
3
x
−
5
x
+
15
=
x
(
x
−
3
)
−
5
(
x
−
3
)
=
(
x
−
3
)
⋅
(
x
−
5
)
x
3
−
8
x
2
+
15
x
=
x
⋅
(
x
−
3
)
⋅
(
x
−
5
)
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