find the zeros for the given polynomial function and give the multiplicity for e

Question

find the zeros for the given polynomial function and give the multiplicity for each zero. state whether the graph crosses the x axis, or touches the x axis and turns around at each zero.
f(x)=x^3 - 4x^2 + 4x
a. the set of zeros is

b. multiplicity at the left most zero

c. multiplicity at the right most zero

d. complete the sentence
    at the left most zero....
     1. the graph crosses the x axis
     2. the graph touches the x axis and turns around

e. complete the sentence
     at the right most zero....
     1. the graph crosses the x axis
     2. the graph touches the x axis and turns around

Explanation / Answer

x^3 - 4x^2 + 4x = 0

Take x out in common :
x(x^2 - 4x + 4) = 0

x(x - 2)(x - 2) = 0

Now, by zero factor property :
x = 0 , x - 2 = 0 , x - 2 = 0

x = 0 , 2 , 2

So, we have :
x = 0, multiplicity = 1
x = 2, multiplicity = 2

a)The set of zeros is : 0,2

b) 1

c) 2

d) Option 1

e) Option 2

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