Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Third-degree, with zeros of $-3,-1$, and 2 , and passes through the point $(3,9)$. Answer 2 Points \[ p(x)= \]

Step 1 ：A polynomial function of degree n with zeros r1, r2, ..., rn can be expressed in the form p(x) = a(x - r1)(x - r2)...(x - rn). In this case, we have a third-degree polynomial with zeros at -3, -1, and 2. So, we can express the polynomial as p(x) = a(x + 3)(x + 1)(x - 2).

Step 2 ：We also know that the polynomial passes through the point (3,9). We can substitute these values into the polynomial to solve for a.

Step 3 ：Substituting x = 3 and y = 9 into the equation, we get 9 = a(3 + 3)(3 + 1)(3 - 2). Solving for a, we get a = 3/8.

Step 4 ：Substituting a = 3/8 back into the polynomial, we get the final polynomial function: \(p(x) = \frac{3}{8}(x + 3)(x + 1)(x - 2)\).

Step 5 ：\(\boxed{p(x) = \frac{3}{8}(x + 3)(x + 1)(x - 2)}\)