Question

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

Answer 1

Answer:

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

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

Observe that

1. $f(-8)=3(-8 + 8)^2(-8 - 8)^3=3*0*(-16)^3=0$

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

2. $f(8)=3(8 + 8)^2(8 - 8)^3=3*16^2*0^3=0$

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.