Solve x^3-3x^2-25x+75

$$x ^ { 3 } - 3 x ^ { 2 } - 25 x + 75$$

Factor

$$\left(x-5\right)\left(x-3\right)\left(x+5\right)$$

Solution Steps

Do the grouping x^{3}-3x^{2}-25x+75=\left(x^{3}-3x^{2}\right)+\left(-25x+75\right), and factor out x^{2} in the first and -25 in the second group.

$$x^{2}\left(x-3\right)-25\left(x-3\right)$$

Factor out common term x-3 by using distributive property.

$$\left(x-3\right)\left(x^{2}-25\right)$$

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.

$$\left(x-5\right)\left(x-3\right)\left(x+5\right)$$

Evaluate

$$\left(x-3\right)\left(x^{2}-25\right)$$