By the way, it's easy to find the Zn roots of the polynomial:
modulus:197$
for i:0 thru 197 do if ratsubst(i,x,x^51+x^22+1)=0 then print (i);
=> 177
rat(177) => -20
divide(x^51+x^22+1,x-177) =>
[yyy,0]
Trying to factor yyy gets you back to the original bug, unsurprisingly....
-s