"Zeros" are the x-values when f(x)=0
x^3-5x^2-3x+15=0 upon slight rearranging of terms...
x^3-3x-5x^2+15=0 now factor first and second pair of terms
x(x^2-3)-5(x^2-3)=0
(x-5)(x^2-3)=0 and if we factor the second parenthetical term as well
(x-5)(x-√3)(x+√3)=0
So if x=-√3, √3, or 5, f(x)=0
Thus the zeros of f(x) are x={-√3, √3, 5}