Solve 20x^5+100x^3+125x

$$20 x ^ { 5 } + 100 x ^ { 3 } + 125 x$$

Factor

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

Solution Steps

Factor out 5.

$$5\left(4x^{5}+20x^{3}+25x\right)$$

Consider 4x^{5}+20x^{3}+25x. Factor out x.

$$x\left(4x^{4}+20x^{2}+25\right)$$

Consider 4x^{4}+20x^{2}+25. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=2x^{2} and b=5.

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

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

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

Evaluate

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