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4\left(4y^{5}+3y^{3}\right)
Factor out 4.
y^{3}\left(4y^{2}+3\right)
Consider 4y^{5}+3y^{3}. Factor out y^{3}.
4y^{3}\left(4y^{2}+3\right)
Rewrite the complete factored expression. Polynomial 4y^{2}+3 is not factored since it does not have any rational roots.