Solve x^5+20x^3+100x

$$x ^ { 5 } + 20 x ^ { 3 } + 100 x$$

Factor

$$x\left(x^{2}+10\right)^{2}$$

Solution Steps

Factor out x.

$$x\left(x^{4}+20x^{2}+100\right)$$

Consider x^{4}+20x^{2}+100. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=x^{2} and b=10.

$$\left(x^{2}+10\right)^{2}$$

Rewrite the complete factored expression. Polynomial x^{2}+10 is not factored since it does not have any rational roots.

$$x\left(x^{2}+10\right)^{2}$$

Evaluate

$$x\left(x^{2}+10\right)^{2}$$