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2\left(2d^{3}+2d^{2}+d\right)
Factor out 2.
d\left(2d^{2}+2d+1\right)
Consider 2d^{3}+2d^{2}+d. Factor out d.
2d\left(2d^{2}+2d+1\right)
Rewrite the complete factored expression. Polynomial 2d^{2}+2d+1 is not factored since it does not have any rational roots.