Solve 25x^7-10x^5+15x^3-5x^3

$$25 x ^ { 7 } - 10 x ^ { 5 } + 15 x ^ { 3 } - 5 x ^ { 3 }$$

Factor

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

Solution Steps

Factor out 5.

$$5\left(5x^{7}-2x^{5}+3x^{3}-x^{3}\right)$$

Consider 5x^{7}-2x^{5}+3x^{3}-x^{3}. Factor out x^{3}.

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

Rewrite the complete factored expression. Polynomial 5x^{4}-2x^{2}+2 is not factored since it does not have any rational roots.

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

Evaluate

$$25x^{7}-10x^{5}+10x^{3}$$

Solution Steps

Combine 15x^{3} and -5x^{3} to get 10x^{3}.

$$25x^{7}-10x^{5}+10x^{3}$$