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\left(x^{2}-2\right)\left(x^{2}+2\right)
Rewrite x^{4}-4 as \left(x^{2}\right)^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right). The following polynomials are not factored since they do not have any rational roots: x^{2}-2,x^{2}+2.