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x\left(x^{4}-16x^{2}+64\right)
Factor out x.
\left(x^{2}-8\right)^{2}
Consider x^{4}-16x^{2}+64. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=x^{2} and b=8.
x\left(x^{2}-8\right)^{2}
Rewrite the complete factored expression. Polynomial x^{2}-8 is not factored since it does not have any rational roots.