Solve 20y^4-80y^3-4y^2+16y

$$20 y ^ { 4 } - 80 y ^ { 3 } - 4 y ^ { 2 } + 16 y$$

Factor

$$4y\left(y-4\right)\left(5y^{2}-1\right)$$

Solution Steps

Factor out 4.

$$4\left(5y^{4}-20y^{3}-y^{2}+4y\right)$$

Consider 5y^{4}-20y^{3}-y^{2}+4y. Factor out y.

$$y\left(5y^{3}-20y^{2}-y+4\right)$$

Consider 5y^{3}-20y^{2}-y+4. Do the grouping 5y^{3}-20y^{2}-y+4=\left(5y^{3}-20y^{2}\right)+\left(-y+4\right), and factor out 5y^{2} in the first and -1 in the second group.

$$5y^{2}\left(y-4\right)-\left(y-4\right)$$

Factor out common term y-4 by using distributive property.

$$\left(y-4\right)\left(5y^{2}-1\right)$$

Rewrite the complete factored expression. Polynomial 5y^{2}-1 is not factored since it does not have any rational roots.

$$4y\left(y-4\right)\left(5y^{2}-1\right)$$

Evaluate

$$4y\left(y-4\right)\left(5y^{2}-1\right)$$