Can you factor the polynomial and use the factored form to find the zeros?

If you have a graphing calculator, type in the P(x) in your Y1 and find a zero (x intercept). This means this equation has a factor of w.e the x intercept was. Then use synthetic division to find out the remainder of the equation.

So for your case:

P(x) = x^4 - 3x^3 + 2x^2
P(1) = 0

Synthetic division:
1  |  1  -3  2  0  0
       |      1  -2  0  0
       |____________
           1  -2  0  0  0

P(x) = (x-1)(x^3-2x^2)
       = x^2(x-1)(x-2)

Therefore your zeroes are:

0, 1, and 2

Are you solving for x? If yes,
 P(x)=x^4-3x^3+2x^2
set it equal to zero.
x^4-3x^3+2x^2=0
in this case, x^2 is common, so we'd factor that out.
x^2(x^2-3x+2)=0
x^2(x-2)(x-1)=0
so, x=0, x=2, x=1 (possible values for x)
All the best

Question Number 1

For this polynomial equation z^4 -3*z^3 +2*z^2  = 0, answer the following questions :
 A. Solve by Factorization

Answer For Question 1

 z^4 -3*z^3 +2*z^2  = 0
 And we get P(z)=z^4 -3*z^3 +2*z^2
 Now, we can look for the roots of P(x) using various Algorithm :

 1A. Solve by Factorization

    z^4 -3*z^3 +2*z^2  = 0
    Separate : ( z^4 -z^3  ) + ( -2*z^3 +2*z^2  ) = 0
    Commutative Law : ( z^4 -2*z^3  ) + ( -z^3 +2*z^2  ) = 0
    Distributive Law : z*( z^3 -2*z^2  ) + -*( z^3 -2*z^2  ) = 0
    Factor : ( z -1 )*( z^3 -2*z^2  ) = 0

    Separate : ( z -1 )*( ( z^3 -2*z^2  ) ) = 0
    Commutative Law : ( z -1 )*( ( z^3  ) + ( -2*z^2  ) ) = 0
    Distributive Law : ( z -1 )*( z*( z^2  ) + -2*( z^2  ) ) = 0
    Factor : ( z -1 )*( z -2 )*( z^2  ) = 0

    Separate : ( z -1 )*( z -2 )*( ( z^2  ) ) = 0
    Commutative Law : ( z -1 )*( z -2 )*( ( z^2  ) + ( 0*z  ) ) = 0
    Distributive Law : ( z -1 )*( z -2 )*( z*( z  ) + 0*( z  ) ) = 0
    Factor : ( z -1 )*( z -2 )*( z +0 )*( z +0 )

   So the Polynomial have 4 roots :
     z1 = 1
     z2 = 2
     z3 = 0
     z4 = 0