Need to calculate:The factorization of x^{3}+3x^2+2x+6

Chesley 2020-12-24 Answered
Need to calculate:The factorization of x3+3x2+2x+6
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Expert Answer

dessinemoie
Answered 2020-12-25 Author has 90 answers
Formula used:
The factors of a polynomial can be find by taking a common factor and this method is called factor by grouping,
ab+ac+bd+cd=a(b+c)+d(b+c)
=(a+d)(b+c)
Or,
abac+bdcd=a(bc)+d(bc)
=(a+d)(bc)
Calculation:
Consider the polynomial x3+3x2+2x+6.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
x3+3x2+2x+6=(x3+3x2)+(2x+6)
=x2(x+3)+2(x+3)
As, (x+3) is the common factor of the polynomial,
The polynomial can be factorized as,
x3+3x2+2x+6=x2(x+3)+2(x+3)
=(x+3)(x2+2)
Therefore, the factorization of the polynomial x3+3x2+2x+6 is (x+3)(x2+2).
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