Question

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

Factor the polynomial and use the factored form to find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

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.