Suppose that the polynomial function \( f \) is defined as follows. \[ f(x)=(x-11)(x-9)(x+4)^{2}(x+11) \] List each zero of \( f \) according to its multiplicity in the categories below. If there is more than one answer for a multiplicity, separate them with commas. \( \begin{array}{l}\text { zero(s) of multiplicity one: } \\ \text { zero(s) of multiplicity two: } \\ \text { zero(s) of multiplicity three: }\end{array} \)

We are given the function   f(x) = (x - 11)(x - 9)(x + 4)²(x + 11). Step 1: Find all the zeros.  • x - 11 = 0 ⟹ x = 11  • x - 9 = 0  ⟹ x = 9  • x + 4 = 0  ⟹ x = -4 (with multiplicity 2 since the factor is squared)  • x + 11 = 0 ⟹ x = -11 Step 2: Identify the multiplicities.  • 11 appears once → multiplicity one.  • 9 appears once → multiplicity one.  • -11 appears once → multiplicity one.  • -4 appears twice → multiplicity two. Arranging the zeros in the required categories: Zero(s) of multiplicity one: 11, 9, -11 Zero(s) of multiplicity two: -4 Zero(s) of multiplicity three: (empty, as none have multiplicity three)