What is the multiple zero and multiplicity of f (x) = x3 - 8x2 + 16x?

zeros

x=0

x=4 with multiplicity 2

Step-by-step explanation:

We need to solve x^3-8x^2+16x=0

Notice each term has a factor of x in common in x^3-8x^2+16x so we can factor it as x (x^2-8x+16)

Now x^2-8x+16 is a quadratic where a=1 ... We can see if it is factorable by looking for two numbers that multiply to be 16 and add up to be - 8 which is - 4 and - 4

So you have x^3-8x^2+16x=0 is equivalent to x (x-4) (x-4) = 0 (this one is in factored form).

x=0

x=4 (multiplicity 2 since you had the factor that is came from occurring twice)