How do i complete factorise x^3+6 in Q[x]?
Now by the rational roots theorem the only rational roots for each of the above binomials is
note that this tells us that 1 is a root of and that is a factor.
You can now factor this by using long division and repeat until the rational roots theorem no longer works.
I hope this helps.
p.s you will find that plus or minus one are the only rational roots.