Solve 60y^4-300y^3-42y^2+210y

$$60 y ^ { 4 } - 300 y ^ { 3 } - 42 y ^ { 2 } + 210 y$$

Factor

$$6y\left(y-5\right)\left(10y^{2}-7\right)$$

Solution Steps

Factor out 6.

$$6\left(10y^{4}-50y^{3}-7y^{2}+35y\right)$$

Consider 10y^{4}-50y^{3}-7y^{2}+35y. Factor out y.

$$y\left(10y^{3}-50y^{2}-7y+35\right)$$

Consider 10y^{3}-50y^{2}-7y+35. Do the grouping 10y^{3}-50y^{2}-7y+35=\left(10y^{3}-50y^{2}\right)+\left(-7y+35\right), and factor out 10y^{2} in the first and -7 in the second group.

$$10y^{2}\left(y-5\right)-7\left(y-5\right)$$

Factor out common term y-5 by using distributive property.

$$\left(y-5\right)\left(10y^{2}-7\right)$$

Rewrite the complete factored expression. Polynomial 10y^{2}-7 is not factored since it does not have any rational roots.

$$6y\left(y-5\right)\left(10y^{2}-7\right)$$

Evaluate

$$6y\left(y-5\right)\left(10y^{2}-7\right)$$