Form a polynomial whose real zeros and degree are given. \( -3,-2,1,3 ; \) degree: 4 Zeros \( \begin{array}{l}\text { Type a polynomial with integer coefficients and a leading coefficient of } 1 . \\ f(x)=\square \text { (Simplify your answer.) }\end{array} \)

To form a polynomial with real zeros at \( -3, -2, 1, \) and \( 3 \) and a leading coefficient of \( 1 \), we start by using the fact that if \( r \) is a zero of the polynomial, then \( (x - r) \) is a factor. So, we can write: \[ f(x) = (x + 3)(x + 2)(x - 1)(x - 3) \] Now, let's multiply these factors together. First, we can pair them for easier multiplication: \[ f(x) = [(x + 3)(x - 3)][(x + 2)(x - 1)] \] Calculating each pair: \[ (x + 3)(x - 3) = x^2 - 9 \] \[ (x + 2)(x - 1) = x^2 + x - 2 \] Now, we can multiply these two results together: \[ f(x) = (x^2 - 9)(x^2 + x - 2) \] Using the distributive property (also known as the FOIL method for polynomials): \[ f(x) = x^2(x^2 + x - 2) - 9(x^2 + x - 2) \] \[ = x^4 + x^3 - 2x^2 - 9x^2 - 9x + 18 \] \[ = x^4 + x^3 - 11x^2 - 9x + 18 \] Thus, the polynomial with the given zeros and degree is: \[ f(x) = x^4 + x^3 - 11x^2 - 9x + 18 \]