Solve x^3+8x-5x^2-40

$$x ^ { 3 } + 8 x - 5 x ^ { 2 } - 40$$

Factor

$$\left(x-5\right)\left(x^{2}+8\right)$$

Solution Steps

Do the grouping x^{3}+8x-5x^{2}-40=\left(x^{3}+8x\right)+\left(-5x^{2}-40\right), and factor out x in the first and -5 in the second group.

$$x\left(x^{2}+8\right)-5\left(x^{2}+8\right)$$

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.

$$\left(x^{2}+8\right)\left(x-5\right)$$

Evaluate

$$\left(x-5\right)\left(x^{2}+8\right)$$