What is the multiple zero and multiplicity of f (x) = x^3-8x^2+16x?

Multiplicity is how many times a root repeats

factor

x (x²-8x+16)

what times wat = 16 and adds to - 8

-4 and - 4

x (x-4) (x-4)

x (x-4) ²

set to zero

x=0

x-4=0

x=4

roots are 0 ad 4

4 repeats 2 times, so has a multiplicty of 2

so

roots are 0, and 4 multiplicity 2