A polynomial is reducibble in Z[x] if and only if it is reducible in Q[x].
y^2-18y-175=0 where y=x^6.
Find zeros and hence find the factors,
Those two polyonomial are irreducible in Z[x].
x^3-25 has no zero (and has degree at most three).
x^3+7 has no zero (and has degree at most three).