What are the zeroes of the function? What are their multiplicities?

= x4 - 4x3 + 3x2

first step is to factor the expression x4 - 4x3 + 3x2. The factor is equal to x2. Hence the factored equation is 0 = x2 * (x2 - 4x + 3). This means one factor should be zero. We factor x2 - 4x + 3. This is factored into (x-3) * (x-1). Hence the factors are 0, 3, and 1.