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

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

-8, multiplicity 2; 8, multiplicity 3

4, multiplicity 1; 8, multiplicity 1; -8, multiplicity 1

-8, multiplicity 3; 8, multiplicity 2

4, multiplicity 1; -8, multiplicity 3; 8, multiplicity 3

a) 8, multiplicity 2; 8, multiplicity 3

Step-by-step explanation:

Remember that a is a zero of the polynomial f(x) if f(a)=0 and has multiplicity n if the termn (x-a) is n times in the factorization of f(x).

We have that

Observe that

1.

and (x+8) appear two times in the factorization of f(x). Then -8 is a zero of f(x) with multiplicity 2.

2.

and and (x - 8) appear three times in the factorization of f(x). Then 8 is a zero of f(x) with multiplicity 3.

Since f(x) has degree 5 and the sum of the multiplicities is 5 then f(x) hasn't more zeros.

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