Integral Domains: Products of Irreducibles

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I'm suppose to find an integral domain where NOT every element (not a unit) is expressible as a finite product of irreducibles.

I'm not sure where to begin, actually. So perhaps someone can give me a tip, and we can start working our way through this. Thanks..
 
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Thank you anyway, all. Since I have other algebra problems that I need help on, I'm going to include this problem in another thread, joining all the problems.
 
closed...see "ALGEBRA PROBLEMS"
 
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