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

Need to calculate:The factorization of $3{x}^{3}+2{x}^{2}+3x+2$.
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Formula used:
The factors of a polynomial can be find by taking a common factor and this method is calledcfactor by grouping,
$abac+bd+cd=a\left(b+c\right)+d\left(b+c\right)$
$=\left(a+d\right)\left(b+c\right)$
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 $3{x}^{3}+2{x}^{2}+3x+2$.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
$3{x}^{3}+2{x}^{2}+3x+2=\left(3{x}^{3}+2{x}^{2}\right)+\left(3x+2\right)$
$={x}^{2}\left(3x+2\right)+1\left(3x+2\right)$
As, $\left(3x+2\right)$ is the common factor of the polynomial,
The polynomial can be factorized as,
${x}^{2}\left(3x+2\right)+1\left(3x+2\right)=\left(3x+2\right)\left({x}^{2}+1\right)$
Therefore, the factorization of the polynomial $3{x}^{3}+2{x}^{2}+3x+2$ is $\left(3x+2\right)\left({x}^{2}+1\right)$.