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

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

Factor

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

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.

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

Evaluate

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