Solve x^3+8x+x^2+8

$$x ^ { 3 } + 8 x + x ^ { 2 } + 8$$

Factor

$$\left(x+1\right)\left(x^{2}+8\right)$$

Solution Steps

Do the grouping x^{3}+8x+x^{2}+8=\left(x^{3}+8x\right)+\left(x^{2}+8\right), and factor out x in x^{3}+8x.

$$x\left(x^{2}+8\right)+x^{2}+8$$

Factor out common term x^{2}+8 by using distributive property. Polynomial x^{2}+8 is not factored since it does not have any rational roots.

$$\left(x^{2}+8\right)\left(x+1\right)$$

Evaluate

$$\left(x+1\right)\left(x^{2}+8\right)$$