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5\left(5q^{8}+8q\right)
Factor out 5.
q\left(5q^{7}+8\right)
Consider 5q^{8}+8q. Factor out q.
5q\left(5q^{7}+8\right)
Rewrite the complete factored expression. Polynomial 5q^{7}+8 is not factored since it does not have any rational roots.