first we find the factors
a^3-8 is the differnce between 2 perfect cubes and is factored out to
(a-2)(a^2+2a+4)
the factors are (a-2) and (a^2+2a+4)
a^4+16
this is not factorable, unless you mistiped it and it was really a^4-16
the factor is 1
a^3+2a^2+4a
factor out the a
a(a^2+2a+4)
this is the most factored out form
the factors are (a) and (a^2+2a+4)
there are no common factors except 1 so 1 is the answer
