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ab\left(6a^{4}+9a-a\right)
Factor out ab.
a\left(6a^{3}+8\right)
Consider 6a^{4}+9a-a. Factor out a.
6a^{3}+8
Consider 6a^{3}+9-1. Multiply and combine like terms.
2\left(3a^{3}+4\right)
Consider 6a^{3}+8. Factor out 2.
2aba\left(3a^{3}+4\right)
Rewrite the complete factored expression. Polynomial 3a^{3}+4 is not factored since it does not have any rational roots.