Solution
For this case we have the following polynomial:
[tex]f(x)=x^3+4x^2+36[/tex]
If x-4 is a factor then x=4 is a root of the polynomial but we can see that:
[tex]f(4)\ne0[/tex]
Then we can conclude that x=4 is not a root
Possible roots for this case are:
x= -5.28760
