Factor
\left(10x^{2}+1\right)\left(100x^{4}-10x^{2}+1\right)
Evaluate
1000x^{6}+1
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\left(10x^{2}+1\right)\left(100x^{4}-10x^{2}+1\right)
Rewrite 1+1000x^{6} as \left(10x^{2}\right)^{3}+1^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right). The following polynomials are not factored since they do not have any rational roots: 100x^{4}-10x^{2}+1,10x^{2}+1.
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