vestirme4

2020-11-23

Need to calculate:The factorization of $2{x}^{3}-8{x}^{2}-9x+36$ .

Theodore Schwartz

Skilled2020-11-24Added 99 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,

$ab-ac+bd-cd=a(b\u2014c)+d(b-c)$

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

Calculation:

Consider the polynomial$2{x}^{3}-8{x}^{2}-9x+36$ .

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

$2{x}^{3}-8{x}^{2}-9x+36=(2{x}^{3}-8{x}^{2})-(9x-36)$

$=2{x}^{2}(x-4)-9(x-4)$

As,$(x-4)$ is the common factor of the polynomial,

The polynomial can be factorized as,

$2{x}^{2}(x-4)-9(x-4)=(x-4)(2{x}^{2}-9)$

Therefore, the factorization of the polynomial$2{x}^{3}-8{x}^{2}-9x+36$ is $(x-4)(2{x}^{2}-9)$ .

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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