Chesley

2020-12-24

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

dessinemoie

Skilled2020-12-25Added 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,

$ab\u2014ac+bd\u2014cd=a(b\u2014c)+d(b-c)$

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

Calculation:

Consider the polynomial${x}^{3}+3{x}^{2}+2x+6$ .

This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,

${x}^{3}+3{x}^{2}+2x+6=(x3+3{x}^{2})+(2x+6)$

$={x}^{2}(x+3)+2(x+3)$

As,$(x+3)$ is the common factor of the polynomial,

The polynomial can be factorized as,

${x}^{3}+3{x}^{2}+2x+6={x}^{2}(x+3)+2(x+3)$

$=(x+3)({x}^{2}+2)$

Therefore, the factorization of the polynomial${x}^{3}+3{x}^{2}+2x+6$ is $(x+3)({x}^{2}+2)$ .

The factors of a polynomial can be find 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 find by factor by grouping as,

As,

The polynomial can be factorized as,

Therefore, the factorization of the polynomial

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

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