F(x) = x^3 - 3x^2 + 4 = 0

for the equation given, 2 has a multiplicity of

1
2
3

The given polynomial is f(x) = x³ - 3x² + 4 = 0

x=2 is a zero with a multiplicity of 2, therefore (x - 2)² should be a factor of f(x).
Perform synthetic division with (x-2).

2 |  1   -3    0   4
            2  -2  -4
   
      1   -1    -2   0
Therefore f(x) = (x-2)(x² - x - 2)

Perform another synthetic division on x² - x - 2  (or factorize).

2 |  1   -1   -2
           2    2
 
      1    1     0
Therefore f(x) = (x-2)(x-2)(x+1) = (x-2)²(x+1)

Note:
If you do not know synthetic division, use long division.
For example,
                     x²  -  x  -  2
       
x-2  |  x³  -  3x²   +   0x   + 4
          x³  -  2x²
         
                 - x²   +  0x   + 4
                 - x²   +  2x
                 
                          - 2x + 4
                          - 2x + 4

 f(x) = (x+1)(x-2)²

The correct answer is: b