Find a polynomial of the specified degree that has the given zeros. Degree \( 3 ; \) zeros \( -2,2,4 \) \( P(x)=\square \)

To construct a polynomial of degree 3 with the given zeros \(-2\), \(2\), and \(4\), we can use the fact that if \(r\) is a root, then \((x - r)\) is a factor of the polynomial. Therefore, the polynomial can be expressed as: \[ P(x) = (x + 2)(x - 2)(x - 4). \] Now, we can expand this expression: 1. First, multiply \((x + 2)\) and \((x - 2)\): \[ (x + 2)(x - 2) = x^2 - 4. \] 2. Next, multiply the result by \((x - 4)\): \[ P(x) = (x^2 - 4)(x - 4) = x^3 - 4x^2 - 4x + 16. \] Thus, the polynomial is: \[ P(x) = x^3 - 4x^2 - 4x + 16. \]