generals336

2021-01-06

Need to calculate:The factorization of ${x}^{3}+8{x}^{2}-3x-24$ .

gwibdaithq

Skilled2021-01-07Added 84 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,

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

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

Calculation:

Consider the polynomial${x}^{3}+8{x}^{2}\u20143x\u201424$ .

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

${x}^{3}+8{x}^{2}\u20143x\u201424=({x}^{3}+8{x}^{2})\u2014(3x+24)$

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

As,$(x+8)$ is the common factor of the polynomial,

The polynomial can be factorized as,

${x}^{2}(x+8)\u20143(x+8)=(x+8)({x}^{-3})$

Therefore, the factorization of the polynomial${x}^{3}+8{x}^{2}\u20143x\u201424\text{}is\text{}(x+8)({x}^{2}-3)$ .

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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