1. **State the problem:** We need to find all x-intercepts of the function $$f(x) = x^5 - 36x^3$$. The x-intercepts occur where $$f(x) = 0$$. 2. **Set the function equal to zero:** $$x^5 - 36x^3 = 0$$ 3. **Factor the expression:** First, factor out the greatest common factor, which is $$x^3$$: $$x^3(x^2 - 36) = 0$$ 4. **Apply the zero product property:** For the product to be zero, either $$x^3 = 0$$ or $$x^2 - 36 = 0$$. 5. **Solve each equation:** - From $$x^3 = 0$$, we get $$x = 0$$. - From $$x^2 - 36 = 0$$, add 36 to both sides: $$x^2 = 36$$ 6. **Take the square root of both sides:** $$x = \pm \sqrt{36}$$ $$x = \pm 6$$ 7. **List all x-intercepts:** $$x = -6, 0, 6$$ **Final answer:** The x-intercepts of the function are $$x = -6, 0, 6$$.