Solve 3x^5-18x^3+27x

$$3 x ^ { 5 } - 18 x ^ { 3 } + 27 x$$

Factor

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

Solution Steps

Factor out 3.

$$3\left(x^{5}-6x^{3}+9x\right)$$

Consider x^{5}-6x^{3}+9x. Factor out x.

$$x\left(x^{4}-6x^{2}+9\right)$$

Consider x^{4}-6x^{2}+9. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=x^{2} and b=3.

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

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

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

Evaluate

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