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\left(6y^{2}-11\right)\left(6y^{2}+11\right)
Rewrite 36y^{4}-121 as \left(6y^{2}\right)^{2}-11^{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: 6y^{2}-11,6y^{2}+11.