Question

Factorizar x^7+x^5-1
Procedimiento por favor

Answer 1

$x^7+x^5-1\\\\ x^7+\underline{x^6-x^6}+x^5+\underline{x^5-x^5}+\underline{x^4-x^4}+\underline{x^3-x^3}+\underline{x^2-x^2}+\underline{x-x}-1\\\\ x^7-x^6+x^5+x^6-x^5+x^4+x^5-x^4+x^3-x^3+x^2-x-x^2+x-1\\\\ \underbrace{x^7-x^6+x^5}_{x^5(x^2-x+1)}+\underbrace{x^6-x^5+x^4}_{x^4(x^2-x+1)}+\underbrace{x^5-x^4+x^3}_{x^3(x^2-x+1)}\underbrace{-x^3+x^2-x}_{-x(x^2-x+1)}\underbrace{-x^2+x-1}_{-(x^2-x+1)}\\\\ (x^2-x+1)(x^5+x^4+x^3-x-1)\\\\ \boxed{x^7+x^5-1=(x^2-x+1)(x^5+x^4+x^3-x-1)}$