Solve 500x^15+108x^9

$$500 x ^ { 15 } + 108 x ^ { 9 }$$

Factor

$$4\left(5x^{2}+3\right)\left(25x^{4}-15x^{2}+9\right)x^{9}$$

Solution Steps

Factor out 4.

$$4\left(125x^{15}+27x^{9}\right)$$

Consider 125x^{15}+27x^{9}. Factor out x^{9}.

$$x^{9}\left(125x^{6}+27\right)$$

Consider 125x^{6}+27. Rewrite 125x^{6}+27 as \left(5x^{2}\right)^{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).

$$\left(5x^{2}+3\right)\left(25x^{4}-15x^{2}+9\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: 5x^{2}+3,25x^{4}-15x^{2}+9.

$$4x^{9}\left(5x^{2}+3\right)\left(25x^{4}-15x^{2}+9\right)$$

Evaluate

$$500x^{15}+108x^{9}$$