Final answer:
The zeros of the function p(x)=-2x⁴(x+1)³(x-2)² are x = 0 (multiplicity 4), x = -1 (multiplicity 3), and x = 2 (multiplicity 2).
Step-by-step explanation:
The zeros of the function p(x)=-2x⁴(x+1)³(x-2)² can be found by setting p(x) equal to zero and solving for x. We have:
-2x⁴(x+1)³(x-2)² = 0
Since a product is equal to zero if and only if one or more of its factors are equal to zero, we can set each factor equal to zero and solve for x:
x = 0 (multiplicity 4),
x+1 = 0 (multiplicity 3),
x-2 = 0 (multiplicity 2).
Therefore, the zeros of the function p(x)=-2x⁴(x+1)³(x-2)² are x = 0 (multiplicity 4), x = -1 (multiplicity 3), and x = 2 (multiplicity 2).