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**1. The problem statement, all variables and given/known data**

Factor ##x^4-3x^2+9## over the reals

**2. Relevant equations**

**3. The attempt at a solution**

I am factoring this polynomial over the reals. So there are two options. It will either split into two linear factors and an irreducible quadratic, or two irreducible quadratics. I'm really not too sure how to proceed from here... Should I first start looking for a real root?