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
[tex]f(x)=3(x + 8)^2(x - 8)^3[/tex]
Observe that
1. [tex]f(-8)=3(-8 + 8)^2(-8 - 8)^3=3*0*(-16)^3=0[/tex]
and (x+8) appear two times in the factorization of f(x). Then -8 is a zero of f(x) with multiplicity 2.
2. [tex]f(8)=3(8 + 8)^2(8 - 8)^3=3*16^2*0^3=0[/tex]
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.
