\( 1 \leftarrow \begin{array}{l}\text { Form a polynomial whose zeros and degree are given. } \\ \text { Zeros: }-4,4,9 \text {; degree: } 3\end{array} \begin{array}{l}\text { Type a polynomial with integer coefficients and a leading coefficient of } 1 \text { in the box below. } \\ f(x)=\square \text { (Simplify your answer.) }\end{array} \)

To form a polynomial given the zeros -4, 4, and 9, you start by creating factors from each zero. The factors are \( (x + 4) \), \( (x - 4) \), and \( (x - 9) \). Multiply these factors together to get the polynomial: \[ f(x) = (x + 4)(x - 4)(x - 9) \] Now, simplify this step by step. First, notice that \( (x + 4)(x - 4) \) is a difference of squares: \[ (x + 4)(x - 4) = x^2 - 16 \] Now, combine this with the remaining factor \( (x - 9) \): \[ f(x) = (x^2 - 16)(x - 9) \] Distributing the terms gives: \[ f(x) = x^3 - 9x^2 - 16x + 144 \] Finally, combining like terms results in your polynomial: \[ f(x) = x^3 - 9x^2 - 16x + 144 \] So the final answer is: \[ f(x) = x^3 - 9x^2 - 16x + 144 \]