factorize x^3-4x^2+x+6
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Answered by
1
Explanation:
It is usually really, really hard to factorize a cubic function. However, for this polynomial, we can factor by grouping. We try values for splitting the term
−
4
x
2
.
For example, we split it into
−
2
x
2
−
2
x
2
.
The equation becomes this:
(
x
3
−
2
x
2
)
−
(
2
x
2
−
x
−
6
)
. We can factorize each of the expressions in the parentheses:
x
2
(
x
−
2
)
−
(
x
−
2
)
(
2
x
+
3
)
. There is a common factor
(
x
−
2
)
.
Factoring the common factor out, we get
(
x
−
2
)
(
x
2
−
2
x
−
3
)
. We then factorize
x
2
−
2
x
−
3
to
(
x
−
3
)
(
x
+
1
)
.
The fully factored form is then
(
x
−
2
)
(
x
−
3
)
(
x
+
1
)
.
Answered by
1
Answer:
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