What are the solutions of the equation x6 + 6x3 + 5 = 0? Use factoring to solve. mc017-1.jpg and x = 1 mc017-2.jpg and x = –1 mc017-3.jpg and x = –1 mc017-4.jpg and x = 1

We are given equation :[tex]x^6+6x^3+5=0[/tex][tex]Use\:the\:rational\:root\:theorem[/tex][tex]\mathrm{Therefore,\:we\:need\:to\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:5}{1}[/tex][tex]-\frac{1}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+1[/tex][tex]\mathrm{Compute\:}\frac{x^6+6x^3+5}{x+1}\mathrm{\:to\:get\:the\:rest\:of\:the\:eqution:\quad }x^5-x^4+x^3+5x^2-5x+5[/tex]Therefore, final factored form it [tex]x^6\:+\:6x^3\:+\:5=\left(x+1\right)\left(x^5-x^4+x^3+5x^2-5x+5\right)[/tex]We can't factor it more.Therefore,x+1=0.x=-1.Therefore, the real solution of the equation would be -1.