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

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

Factor

$$-\left(x+3\right)x^{2}\left(x^{2}+1\right)$$

Solution Steps

Factor out x^{2}.

$$x^{2}\left(-x^{3}-3x^{2}-x-3\right)$$

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

$$x^{2}\left(-x-3\right)-x-3$$

Factor out common term -x-3 by using distributive property.

$$\left(-x-3\right)\left(x^{2}+1\right)$$

Rewrite the complete factored expression. Polynomial x^{2}+1 is not factored since it does not have any rational roots.

$$x^{2}\left(-x-3\right)\left(x^{2}+1\right)$$

Evaluate

$$-\left(x+3\right)x^{2}\left(x^{2}+1\right)$$