Question 1077099: I am supposed to find the zeros of  and I know there are going to be complex zeroes, I just do not know how to start factoring it so that I can solve it. My textbook doesn't help much and I would truly appreciate the help.
Found 2 solutions by Edwin McCravy, Alan3354:
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
A potential zero is any positive or negative fraction
whose numerator is a factor of 8 (the last term), and whose
denominator is a factor of 3 the leading coefficient.
So the potential zeros are positive or negative fractions
with numerator 1,2,4, or 8 and denominator 1 or 3.
They are ±1,±1/3,±2,±2/3,±4,±4/3,±8,±8/3
Try -2/3 and synthetic division.
If you have trouble, tell me in the thank-you note form
below and I'll get back to you by email. (No charge ever).
Edwin
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! I am supposed to find the zeros of and I know there are going to be complex zeroes, I just do not know how to start factoring it so that I can solve it.
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There are no integer factors.
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Look for a fractional zero as Edwin said.
Make an Excel sheet if you have it.
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3x^3-4x^2+8x+8
-2 -48
-1.666666667 -30.33333333
-1.333333333 -16.88888889
-1 -7
-0.666666667 0
-0.333333333 4.777777778
0 8
0.333333333 10.33333333
-2/3 is a zero.
Divide by (3x+2), then solve the quadratic.
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