Solve 40x^5+5x^2

$$40 { x }^{ 5 } +5 { x }^{ 2 }$$

Factor

$$5\left(2x+1\right)x^{2}\left(4x^{2}-2x+1\right)$$

Solution Steps

Factor out 5.

$$5\left(8x^{5}+x^{2}\right)$$

Consider 8x^{5}+x^{2}. Factor out x^{2}.

$$x^{2}\left(8x^{3}+1\right)$$

Consider 8x^{3}+1. Rewrite 8x^{3}+1 as \left(2x\right)^{3}+1^{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).

$$\left(2x+1\right)\left(4x^{2}-2x+1\right)$$

Rewrite the complete factored expression. Polynomial 4x^{2}-2x+1 is not factored since it does not have any rational roots.

$$5x^{2}\left(2x+1\right)\left(4x^{2}-2x+1\right)$$

Evaluate

$$40x^{5}+5x^{2}$$