If one of our zeros is 4, then the factor is x-4. If the second zero is 5i, then the conjugate root theorem says there HAS to be a root that is -5i. So our 3 factors are (x-4)(x+5i)(x-5i). We will FOIL out these factors to get the polynomial. Let's start with the ones that contain the imaginary numbers. Doing that mutliplication we get x^2-25i^2. i^2 is equal to -1, so what that expression simplifies down to is [tex] x^{2} +25[/tex]. Now we will multiply in that last factor of (x-4): [tex](x^2+25)(x-4)[/tex]. FOILing out we have [tex]x^3-4x^2+25x-100[/tex]. There you go!
