factorise x³-4x²+x+6
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Step-by-step explanation:
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)(x2−2x−3)
. We then factorize
x
2−2x−3
to (x−3)(x+1) .
The fully factored form is then
(x−2)(x−3)(x+1)
.
Hope it helps you
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