Question

identify the zeros of the function and their possible multiplicities of the polynomial function.
$f(x) = (x - 3)^3(x + 2)^2$

select one:
a. $-3$ with multiplicity $1$ and $2$ with multiplicity $2$.
b. $3$ with multiplicity $3$ and $-2$ with multiplicity $2$.
c. $-3$ with multiplicity $2$ and $-2$ with multiplicity $2$.
d. $-3$ with multiplicity $3$ and $2$ with multiplicity $2$.

Explanation:

Step1: Find zeros of the function

Set each factor equal to 0:
For $(x-3)=0$, solve for $x$: $x=3$
For $(x+2)=0$, solve for $x$: $x=-2$

Step2: Identify multiplicities

The exponent of $(x-3)$ is 3, so multiplicity of 3 is 3.
The exponent of $(x+2)$ is 2, so multiplicity of $-2$ is 2.

Answer:

B. 3 with multiplicity 3 and $-2$ with multiplicity 2.