Solve y^4+7y^3-5y^2-35y

$$y ^ { 4 } + 7 y ^ { 3 } - 5 y ^ { 2 } - 35 y$$

Factor

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

Solution Steps

Factor out y.

$$y\left(y^{3}+7y^{2}-5y-35\right)$$

Consider y^{3}+7y^{2}-5y-35. Do the grouping y^{3}+7y^{2}-5y-35=\left(y^{3}+7y^{2}\right)+\left(-5y-35\right), and factor out y^{2} in the first and -5 in the second group.

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

Factor out common term y+7 by using distributive property.

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

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

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

Evaluate

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