what are the differences in the resulting factorizations

Questions
,
1

1+x^n+x^m+x^(n+m) and 1+x+x^3+x^4

1+x^3 and 1+x^n

1-x^4 and 1-x^2n

2

If you are looking for more than the Factor function, please explain. Otherwise, this just sounds like homework.

In[2]:= Factor[1+x^n+x^m+x^(n+m)]

              m        n
Out[2]= (1 + x ) (1 + x )