Solve y^3+11y^2-4y-44

$$y ^ { 3 } + 11 y ^ { 2 } - 4 y - 44$$

Factor

$$\left(y-2\right)\left(y+2\right)\left(y+11\right)$$

Solution Steps

Do the grouping y^{3}+11y^{2}-4y-44=\left(y^{3}+11y^{2}\right)+\left(-4y-44\right), and factor out y^{2} in the first and -4 in the second group.

$$y^{2}\left(y+11\right)-4\left(y+11\right)$$

Factor out common term y+11 by using distributive property.

$$\left(y+11\right)\left(y^{2}-4\right)$$

Consider y^{2}-4. Rewrite y^{2}-4 as y^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y-2\right)\left(y+2\right)$$

Rewrite the complete factored expression.

$$\left(y-2\right)\left(y+2\right)\left(y+11\right)$$

Evaluate

$$\left(y+11\right)\left(y^{2}-4\right)$$