2(x - 3)^2 - 3 factories
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How do you factor
x
3
−
2
x
2
−
x
+
2
by grouping?
Algebra Factoring by Grouping
1 Answer
Mahek ☮
Mar 11, 2018
=
(
x
−
1
)
(
x
+
1
)
(
x
−
2
)
Explanation:
x
3
−
2
x
2
−
x
+
2
=
x
3
−
x
−
2
x
2
+
2
Grouping the
1
s
t
2
terms together and the
2
n
d
2
together:
=
x
(
x
2
−
1
)
−
2
(
x
2
−
1
)
=
(
x
2
−
1
)
(
x
−
2
)
Using the identity:
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
=
(
x
2
−
1
2
)
(
x
−
2
)
=
(
x
−
1
)
(
x
+
1
)
(
x
−
2
)
Alternate Method:-
The above method is an easy on to solve this question. For factorizing other cubic polynomials, the following method can be used:
First, by trial and error method, you can find one factor as follows:
x
3
−
2
x
2
−
x
+
2
When replacing 1,
⇒
1
3
−
2
×
1
2
−
1
+
2
⇒
1
−
2
−
1
+
2
⇒
0
So, we get
(
x
−
1
)
as factor.
Then by long division, divide
(
x
−
1
)
by
(
x
3
−
2
x
2
−
x
+
2
)
You get
⇒
(
x
−
1
)
(
x
2
−
x
−
2
)
Then you have to factorize it by splitting the middle term method.
⇒
(
x
−
1
)
[
x
2
+
x
−
2
x
−
2
]
⇒
(
x
−
1
)
[
x
(
x
+
1
)
−
2
(
x
+
1
)
]
⇒
(
x
−
1
)
(
x
+
1
)
(
x
−
2
)
~Hope this helps! :)
Answer link
Related topic
Factoring by Grouping
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