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6\left(5y^{4}+4y^{3}+3y^{2}\right)
Factor out 6.
y^{2}\left(5y^{2}+4y+3\right)
Consider 5y^{4}+4y^{3}+3y^{2}. Factor out y^{2}.
6y^{2}\left(5y^{2}+4y+3\right)
Rewrite the complete factored expression. Polynomial 5y^{2}+4y+3 is not factored since it does not have any rational roots.