Lipossig

2021-02-16

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

ottcomn

Skilled2021-02-17Added 97 answers

Formula used:

The factors of a polynomial can be found by taking a common factor and this method is called factor by grouping,

$ab+ac+bd+cd=a(b+c)+d(b+c)$

$=(a+d)(b+c)$

Or,

$ab-ac+bd-cd=a(b-c)+d(b-c)$

$=(a+d)(b-c)$

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,

$8{x}^{3}+20{x}^{2}+2x+5=(8{x}^{3}+20{x}^{2})+(2x+5)$

$=4{x}^{2}(2x+5)+1(2x+5)$

As,$(2x+5)$ is the common factor of the polynomial,

The polynomial can be factorized as,

$8{x}^{3}+20{x}^{2}+2x+5=4{x}^{2}(2x+5)+1(2x+5)$

$=(2x+5)(4{x}^{2}+1)$

Therefore, the factorization of the polynomial is$(2x+5)(4{x}^{2}+1)$ .

The factors of a polynomial can be found by taking a common factor and this method is called factor by grouping,

Or,

Calculation:

Consider the polynomial

This is a four term polynomial, factorization of this polynomial can be found by factor bycgrouping as,

As,

The polynomial can be factorized as,

Therefore, the factorization of the polynomial is

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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