Solve 3x^4+81x

$$3 { x }^{ 4 } +81x$$

Factor

$$3x\left(x+3\right)\left(x^{2}-3x+9\right)$$

Solution Steps

Factor out 3.

$$3\left(x^{4}+27x\right)$$

Consider x^{4}+27x. Factor out x.

$$x\left(x^{3}+27\right)$$

Consider x^{3}+27. Rewrite x^{3}+27 as x^{3}+3^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

$$\left(x+3\right)\left(x^{2}-3x+9\right)$$

Rewrite the complete factored expression. Polynomial x^{2}-3x+9 is not factored since it does not have any rational roots.

$$3x\left(x+3\right)\left(x^{2}-3x+9\right)$$

Evaluate

$$3x\left(x^{3}+27\right)$$