By the polynomial remainder theorem, [tex]x+1[/tex] is a factor of [tex]x^{65}+2x^{58}-3x^{35}+x^6-4[/tex] if the value of the latter polynomial is zero when [tex]x=-1[/tex].
You have
[tex](-1)^{65}+2(-1)^{58}-3(-1)^{35}+(-1)^6-4=-1+2+3+1-4=1\neq0[/tex]
so [tex]x+1[/tex] is not a factor.
