- #1

cepheid

Staff Emeritus

Science Advisor

Gold Member

- 5,192

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**Algebra--should be simple, but isn't**

I'm having trouble factoring the polynomial:

p(z) = 1 + z + z

^{2}+ z

^{3}+ z

^{4}

I don't know how to factor a quartic except by trial and error. Our prof assured us that we probably wouldn't want to make use of the formula for finding the zeros, even if we had it. He encouraged us to just try out various things like 1, -1, i, -i, etc to see if we could find a zero by inspection. I'm not having any luck with that method. What's the strategy here?