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\left(n^{2}-10\right)\left(n^{2}+10\right)
Rewrite n^{4}-100 as \left(n^{2}\right)^{2}-10^{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: n^{2}-10,n^{2}+10.