Find the zeros of the polynomial function and state the multiplicity of each.
-$$f ( x ) = 2 ( x + 9 ) ^ { 2 } ( x - 9 ) ^ { 3 }$$
A) 4 , multiplicity $1 ; - 9$, multiplicity $3 ; 9$, multiplicity 3
B) $- 9$, multiplicity $3 ; 9$, multiplicity 2
C) $- 9$, multiplicity $2 ; 9$, multiplicity 3
D) 4 , multiplicity $1 ; 9$, multiplicity $1 ; - 9$, multiplicity 1

Question

Quizplus · Accepted Answer

The zeros of the polynomial are found by setting $f(x) = 0$. The given polynomial has zeros at $x = -9$ and $x = 9$, with multiplicities corresponding to the powers of their factors. $x = -9$ has a multiplicity of 2 because of the squared factor $(x + 9)^2$, and $x = 9$ has a multiplicity of 3 because of the cubed factor $(x - 9)^3$.

Find the Zeros of the Polynomial Function and State the Multiplicity