Kye

2020-11-02

Solve the factorization of ${x}^{12}+{x}^{7}+{x}^{5}+1$

Jaylen Fountain

Skilled2020-11-03Added 169 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${x}^{12}+{x}^{7}+{x}^{5}+1$ .

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

${x}^{12}+{x}^{7}+{x}^{5}+1=({x}^{12}+{x}^{7})({x}^{5}+1)$

$={x}^{7}({x}^{5}+1)+1({x}^{5}+1)$

As,$({x}^{5}+1)$ is the common factor of the polynomial,

The polynomial can be factorized as,

${x}^{7}({x}^{5}+1)+1({x}^{5}+1)=({x}^{5}+1)({x}^{7}+1)$

Therefore, the factorization of the polynomial${x}^{12}+{x}^{7}+{x}^{5}+1$ is $({x}^{5}+1)({x}^{7}+1)$ .

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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