Question 18, 2.3.25
Part 1 of 3
points
Points: 0 of 1
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosse the $x$-axis or touches the $x$-axis and turns around at each zero.
$$f(x)=-2(x-6)(x-1{)}^2$$

Determine the zero(s)
The zero(s) is/are $◻$
(Type integers or decimals. Use a comma to separate answers as needed.)

Step 1 ：The zeros of a polynomial function are the values of x for which the function equals zero. In this case, the function is given in factored form, so we can see that the zeros are the values of x that make each factor equal to zero. The factors are $(x-6)$ and $(x-1)$, so the zeros are x=6 and x=1.

Step 2 ：The multiplicity of a zero is the number of times that factor appears in the function. In this case, the factor $(x-1)$ appears twice, so the zero x=1 has multiplicity 2, and the factor $(x-6)$ appears once, so the zero x=6 has multiplicity 1.

Step 3 ：Final Answer: The zero(s) is/are $\boxed{{\displaystyle x=1}}$ with multiplicity 2 and $\boxed{{\displaystyle x=6}}$ with multiplicity 1.