Question

find the zeros of the function. state the multiplicity of multiple zeros. f(x)=(x - 1)^3(x - 5) the distinct zeros are. (use a comma to separate answers.)

Explanation:

Step1: Set function equal to 0

$f(x) = (x-1)^3(x-5) = 0$

Step2: Solve each factor for x

For $(x-1)^3=0$: $x-1=0 \implies x=1$
For $(x-5)=0$: $x-5=0 \implies x=5$

Step3: Identify multiplicities

The zero $x=1$ has multiplicity 3; $x=5$ has multiplicity 1.

Answer:

The distinct zeros are $1, 5$

• Zero $1$ has multiplicity 3
• Zero $5$ has multiplicity 1