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

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

3x��x��3x+1

Factor x� out of the first two terms:

x�(3x-1)-3x+1

Factor -1 out of the last two terms:

x�(3x-1)-1(3x-1)

Factor out (3x-1)

(3x-1)(x�-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=

The zeros are , 1, and -1

Edwin

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