Question 45356
First, find a common factor in each of the three terms. This would be {{{3z^2}}} so factor this out.

{{{3z^2(15z^4+16z^2+4)}}}

Next, factor the parentheses. 
{{{(15z^4+16z^2+4) = (3z^2+2)(5z^2+2)}}} So now you have:

{{{45z^6+48z^4+12z^2 = 3z^2(3z^2+2)(5z^2+2)}}}