What are the zeros of the polynomial function? \( f(x)=x^{3}-x^{2}-4 x+4 \) Select each correct answer. -3 -2 -1 0 -1 2

To find the zeros of the polynomial function \( f(x) = x^{3} - x^{2} - 4x + 4 \), we can start by using the Rational Root Theorem and synthetic division to test possible rational roots. By checking various values, we discover that \( x = 2 \) is indeed a root. After factoring out \( (x - 2) \), we can further explore the remaining quadratic equation to find additional roots. Once we factor the polynomial completely, the zeros we find are \( x = 2 \) and potentially another set of values from the quadratic factor. Therefore, among the options given, \( 2 \) is a correct zero, while the others (-3, -2, -1, and 0) do not satisfy the equation. In practice, finding the zeros of polynomials is crucial, as they can represent critical points in graphs, where the function intersects the x-axis. Understanding these intersections helps in sketching functions and determining their behavior, making this concept a key part of algebra and calculus.