Solve x^3+12x^2+6x+72

$$x ^ { 3 } + 12 x ^ { 2 } + 6 x + 72$$

Factor

$$\left(x+12\right)\left(x^{2}+6\right)$$

Solution Steps

Do the grouping x^{3}+12x^{2}+6x+72=\left(x^{3}+12x^{2}\right)+\left(6x+72\right), and factor out x^{2} in the first and 6 in the second group.

$$x^{2}\left(x+12\right)+6\left(x+12\right)$$

Factor out common term x+12 by using distributive property. Polynomial x^{2}+6 is not factored since it does not have any rational roots.

$$\left(x+12\right)\left(x^{2}+6\right)$$

Evaluate

$$\left(x+12\right)\left(x^{2}+6\right)$$