factorize x^3-4x^2+x+6 using identity
Answers
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Step-by-step explanation:
Answer:
( x − 2 ) ( x − 3 ) ( x + 1 )
Step-by-step 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 ) .
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