1. The problem is to find the x-intercept(s) of a polynomial function. 2. The x-intercept(s) are the points where the graph of the polynomial crosses the x-axis. 3. At these points, the value of the function is zero, so we set the polynomial equal to zero: $$f(x) = 0$$ 4. To find the x-intercepts, solve the equation $$f(x) = 0$$ for $x$. 5. This may involve factoring the polynomial, using the quadratic formula, or other algebraic methods depending on the degree and form of the polynomial. 6. Each solution $x = a$ corresponds to an x-intercept at the point $(a, 0)$. 7. For example, if $$f(x) = x^2 - 4$$, set $$x^2 - 4 = 0$$. 8. Factor: $$(x - 2)(x + 2) = 0$$. 9. Set each factor equal to zero: $$x - 2 = 0$$ or $$x + 2 = 0$$. 10. Solve for $x$: $$x = 2$$ or $$x = -2$$. 11. Therefore, the x-intercepts are at $(2, 0)$ and $(-2, 0)$. This method works for any polynomial function.