Question 43872
Let's see if the expression can be factored. Rewrite it in standard form:
{{{z^2+18z+45}}}
The factors will look like: (z+a)(z+b) and you would like to have:
a*b = 45 and
a+b = 18

The factors of the first term are {{{z*z = z^2}}}
The possible factors (a & b) of the last term are:
3*15 = 45
5*9 = 45

Now you want the factors (a & b) of the last term to add up to 18 (a+b = 18) so you can get the middle term of your original expression (18z).
It looks like 3+15 = 18, so a = 3 and b = 15
So the factors of:
{{{z^2+18z+45 = (z+3)(z+15)}}}