Need to calculate:The factorization of ${x}^{3}-7{x}^{2}+4x-28$ .

sanuluy
2021-01-10
Answered

Need to calculate:The factorization of ${x}^{3}-7{x}^{2}+4x-28$ .

You can still ask an expert for help

brawnyN

Answered 2021-01-11
Author has **91** 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${x}^{3}\u20147{x}^{2}+4x-28$ .

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

${x}^{3}-7{x}^{2}+4x-28=({x}^{3}-7{x}^{2})+(4x-28)$

$={x}^{2}(x-7)+4(x-7)$

As,$(x-7)$ is the common factor of the polynomial,

The polynomial can be factorized as,

${x}^{3}-7{x}^{2}+4x-28={x}^{2}(x-7)+4(x-7)$

$=(x-7)({x}^{2}+4)$

Therefore, the factorization of the polynomial is$(x\u20147)({x}^{2}+4)$ .

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 find by factor by grouping as,

As,

The polynomial can be factorized as,

Therefore, the factorization of the polynomial is

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