Khaleesi Herbert

2021-02-21

Solve. The factorization of the polynomial is $\left(3x+2\right)\left(2{x}^{2}+1\right)$.
Given Information:
The provided polynomial is $6{x}^{3}+4{x}^{2}+3x+2$.

crocolylec

Formula used:
The factors of a polynomial can be found by taking a common factor and this method is called factor by grouping,
$ab+ac+bd+cd=a\left(b+c\right)+d\left(b+c\right)$
$=\left(a+d\right)\left(b+c\right)$
Or,
$ab-ac+bd-cd=a\left(b-c\right)+d\left(b-c\right)$
$=\left(a+d\right)\left(b-c\right)$
Calculation:
Consider the polynomial $6{x}^{3}+4{x}^{2}+3x+2$.
This is a four term polynomial, factorization of this polynomial can be found by factor by grouping as,
$6{x}^{3}+4{x}^{2}+3x+2=\left(6{x}^{3}+4{x}^{2}\right)+\left(3x+2\right)$
$=2{x}^{2}\left(3x+2\right)+1\left(3x+2\right)$
As,$\left(3x+2\right)$ is the common factor of the polynomial,
The polynomial can be factorized as,
$6{x}^{3}+4{x}^{2}+3x+2=2{x}^{2}\left(3x+2\right)+1\left(3x+2\right)$
$=\left(3x+2\right)\left(2{x}^{2}+1\right)$
Therefore, the factorization of the polynomial is $\left(3x+2\right)\left(2{x}^{2}+1\right)$.

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