Solve x^3+x^2-25x-25

$${ x }^{ 3 } + { x }^{ 2 } -25x-25$$

Factor

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

Solution Steps

Do the grouping x^{3}+x^{2}-25x-25=\left(x^{3}+x^{2}\right)+\left(-25x-25\right), and factor out x^{2} in the first and -25 in the second group.

$$x^{2}\left(x+1\right)-25\left(x+1\right)$$

Factor out common term x+1 by using distributive property.

$$\left(x+1\right)\left(x^{2}-25\right)$$

Consider x^{2}-25. Rewrite x^{2}-25 as x^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-5\right)\left(x+5\right)$$

Rewrite the complete factored expression.

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

Evaluate

$$\left(x+1\right)\left(x^{2}-25\right)$$