# Need to calculate:The factorization of 8x^{3}+20x^{2}+2x+5.

Need to calculate:The factorization of $8{x}^{3}+20{x}^{2}+2x+5$.
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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 $8{x}^{3}+20{x}^{2}+2x+5$.
This is a four term polynomial, factorization of this polynomial can be found by factor bycgrouping as,
$8{x}^{3}+20{x}^{2}+2x+5=\left(8{x}^{3}+20{x}^{2}\right)+\left(2x+5\right)$
$=4{x}^{2}\left(2x+5\right)+1\left(2x+5\right)$
As, $\left(2x+5\right)$ is the common factor of the polynomial,
The polynomial can be factorized as,
$8{x}^{3}+20{x}^{2}+2x+5=4{x}^{2}\left(2x+5\right)+1\left(2x+5\right)$
$=\left(2x+5\right)\left(4{x}^{2}+1\right)$
Therefore, the factorization of the polynomial is $\left(2x+5\right)\left(4{x}^{2}+1\right)$.