Answer
The polynomial function f(x) = (x+2)^2(x+4)(x+1)^3 has the roots: -2 with multiplicity 2, 4 with multiplicity 1, and -1 with multiplicity 3. To determine the roots, we set each factor equal to zero. Since the function is given in its factored form, we can directly find the roots and their respective multiplicities. For (x+2)^2, setting it to zero yields x = -2 with a multiplicity of 2. For (x+4), setting it to zero gives x = -4 with a multiplicity of 1. Lastly, for (x+1)^3, we have x = -1 with a multiplicity of 3. Thus, the roots of the polynomial function are: -2 (multiplicity 2), 4 (multiplicity 1), and -1 (multiplicity 3).
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