Question

Find the zeros of the polynomial function and state the multiplicity of each:

f(x)=(x+8)^2(x-8)^3

Answer 1

x = -8 (with multiplicity 2) and x = 8 (with multiplicity 3).

Explanation:

To find the zeros of the polynomial function f(x) = (x + 8)^2(x - 8)^3, we need to find the values of x that make f(x) equal to zero. This occurs when any of the factors is equal to zero.

Setting each factor equal to zero, we get:

x + 8 = 0, which gives x = -8 (with multiplicity 2, since this factor appears twice)

x - 8 = 0, which gives x = 8 (with multiplicity 3, since this factor appears three times)

Therefore, the zeros of the polynomial function f(x) are x = -8 (with multiplicity 2) and x = 8 (with multiplicity 3).