Question 104483
EJ, let's start with what you know. 
Nth degree polynomial with n=3 means
{{{f(x)=ax^3+bx^2+cx+d}}}
Your job is to find a,b,c,d with the rest of the information provided.
{{{f(-4)=0}}}
{{{f(i)=0}}}
{{{f(-3)=60}}}
The problems is you have 4 unknowns (a,b,c,d) and only three equations to solve them with. Let's plug in and see what we find. 
1.{{{f(-4)=a(-4)^3+b(-4)^2+c(-4)+d=0}}}
2.{{{f(i)=a(i)^3+b(i)^2+c(i)+d=0}}}
3.{{{f(-3)=a(-3)^3+b(-3)^2+c(-3)+d=0}}}
Simplifying the equations, gives you
1.{{{-64a+16b-4c+d=0}}}
2. {{{-ia-b+ic+d=0}}}
3.{{{-27a+9b-3c+d=60}}}
where {{{i^2=-1}}} and {{{i^3=-i}}}.
Since you have a complex expression in your second equation, it actually acts as an additional equation. Since both the real part and the complex part of equation 2 have to equal zero, you now have 4 equations with four unknowns.
1.{{{-64a+16b-4c+d=0}}}
2.(Real){{{-b+d=0}}}
3.(Complex){{{-a+c=0}}}
4.{{{-27a+9b-3c+d=60}}}
With those 4 equations, you are able to substitute and find the values for a,b,c,d. 
Good luck and post another question if you get stuck.