SOLUTION: Find all of the zeros of the polynomial 3x3 – x2 – 3x + 1

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Question 472015: Find all of the zeros of the polynomial 3x3 – x2 – 3x + 1
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
3x³–x²–3x+1

Factor x² out of the first two terms:

x²(3x-1)-3x+1

Factor -1 out of the last two terms:

x²(3x-1)-1(3x-1)

Factor out (3x-1)

(3x-1)(x²-1)

Factor the second parenthesis as the difference of two squares:

(3x-1)(x-1)(x+1)

Set each factor = 0

3x-1=0   x-1=0   x+1=0
  3x=1     x=1     x=-1
   x=1%2F3

The zeros are 1%2F3, 1, and -1

Edwin