Solve x^3-6x^2+25x-150

$$x ^ { 3 } - 6 x ^ { 2 } + 25 x - 150$$

Factor

$$\left(x-6\right)\left(x^{2}+25\right)$$

Solution Steps

Do the grouping x^{3}-6x^{2}+25x-150=\left(x^{3}-6x^{2}\right)+\left(25x-150\right), and factor out x^{2} in the first and 25 in the second group.

$$x^{2}\left(x-6\right)+25\left(x-6\right)$$

Factor out common term x-6 by using distributive property. Polynomial x^{2}+25 is not factored since it does not have any rational roots.

$$\left(x-6\right)\left(x^{2}+25\right)$$

Evaluate

$$\left(x-6\right)\left(x^{2}+25\right)$$