[tex]x^5+2x^4-3x^3-6x^2+2x+4=0\\\\x^4(x+2)-3x^2(x+2)+2(x+2)=0\\\\(x+2)(x^4-3x^2+2)=0\\\\(x+2)(x^4-2x^2-x^2+2)=0\\\\(x+2)[x^2(x^2-2)-(x^2-2)]=0\\\\(x+2)(x^2-2)(x^2-1)=0\\\\(x+2)(x-\sqrt2)(x+\sqrt2)(x-1)(x+1)=0\\\\x+2=0\ \ \ \lub\ \ \ x-\sqrt2=0\ \ \ lub\ \ \ x+\sqrt2=0\ \ \ lub\ \ \ x-1=0\ \ \ lub\ \ \ x+1=0\\\\x=-2\ \ \ \ \ \ \ \ \ x=\sqrt2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=-\sqrt2\ \ \ \ \ \ \ \ \ \ \ \ \ x=1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=-1[/tex]