Solve y^3+5y^2-y-5

$$y ^ { 3 } + 5 y ^ { 2 } - y - 5$$

Factor

$$\left(y-1\right)\left(y+1\right)\left(y+5\right)$$

Solution Steps

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

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

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

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

Consider y^{2}-1. Rewrite y^{2}-1 as y^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y-1\right)\left(y+1\right)$$

Rewrite the complete factored expression.

$$\left(y-1\right)\left(y+1\right)\left(y+5\right)$$

Evaluate

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