Question

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

Answer 1

1. Factor P (x) = x^4 - 4x^3 + 3x^2:

1a. Factor out the GCF or x^2:

    P (x) = x^2 (x^2- 4x + 3)

1b. Factor the trinomial.  What multiplies to make 3 and adds to make -4?  

     (-1)+(-3) = -4   and    (-1)(-3) = 3

    P (x) = x^2 (x-1) (x-3)

2. Find the zeros be setting each factor equal to 0:

    x^2 = 0 if x=0, with multiplicity 2

    x-1 = 0 if x=1

    x-3 = 0 if x=3

Your zeros are 0, 0, 1, and 3.