Factor $x^{35}+x^{19}+x^{17}-x^2+1$ I tried to factor $x^{35}+x^{19}+x^{17}-x^2+1$ and I can see that $\omega$ and $\omega^2$ are two conjugate roots of $x^{35}+x^{19}+x^{17}-x^2+1$. So I divide it by $x^2+x+1$ and the factorization comes to the following
$$(x^2+x+1)(x^{33}-x^{32}+x^{30}-x^{29}+x^{27}-x^{26}+x^{24}-x^{23}+x^{21}-x^{20}+x^{18}-x^{16}+2x^{15}-x^{14}-x^{13}+2x^{12}-x^{11}-x^{10}+2x^{9}-x^{8}-x^{7}+2x^6-x^5-x^4+2x^3-x^2-x+1)$$
I couldn't go further. My question is is it end here or there is a simple way to do further?

I think if we simply add and then subtract $x^{18}$ and x this factorization becomes easier.
$x^{35} + x^{19} + x^{17} - x^{2} +1 = x^{35}- x^{18}+ x^{17}+ x^{19}- x^{2}+x+ x^{18}- x+ 1$ = $x^{17}(x^{18}-x+1)+ x(x^{18}-x +1)+(x^{18}- x +1)$= $(x^{18}-x+1)(x^{17}+x+1)$. 
Now it is easy to see that omega is a root of $x^{17}+x+1$ which means $x^{2}+x+1$ is a factor of $x^{17}+x+1$. Now applying vanishing method on $x^{17}+x+1$ we easily get 
$x^{17}+x+1$ = $(x^{2}+x+1)(x^{15}-x^{14}+x^{12}-x^{11}+x^{9}-x^{8}+x^{6}-x^{5}+x^{3}-x^{2}+1$).So our required solution is
 $x^{35}+x^{19}+x^{17}-x^{2}+1=(x^{18}-x+1)(x^{2}+x+1)(x^{15}-x^{14}+x^{12}-x^{11}+x^{9}-x^{8}+x^{6}-x^{5}+x^{3}-x^{2}+1)$
