Solve x^4+5x^2-4x^3-20x

$$x ^ { 4 } + 5 x ^ { 2 } - 4 x ^ { 3 } - 20 x$$

Factor

$$x\left(x-4\right)\left(x^{2}+5\right)$$

Solution Steps

Factor out x.

$$x\left(x^{3}+5x-4x^{2}-20\right)$$

Consider x^{3}+5x-4x^{2}-20. Do the grouping x^{3}+5x-4x^{2}-20=\left(x^{3}+5x\right)+\left(-4x^{2}-20\right), and factor out x in the first and -4 in the second group.

$$x\left(x^{2}+5\right)-4\left(x^{2}+5\right)$$

Factor out common term x^{2}+5 by using distributive property.

$$\left(x^{2}+5\right)\left(x-4\right)$$

Rewrite the complete factored expression. Polynomial x^{2}+5 is not factored since it does not have any rational roots.

$$x\left(x^{2}+5\right)\left(x-4\right)$$

Evaluate

$$x\left(x-4\right)\left(x^{2}+5\right)$$