Solve x^8-5x^4/2-5x^3

$$x ^ { 8 } - \frac { 5 x ^ { 4 } } { 2 } - 5 x ^ { 3 }$$

Factor

$$\frac{x^{3}\left(2x^{5}-5x-10\right)}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{2x^{8}-5x^{4}-10x^{3}}{2}$$

Consider 2x^{8}-5x^{4}-10x^{3}. Factor out x^{3}.

$$x^{3}\left(2x^{5}-5x-10\right)$$

Rewrite the complete factored expression. Polynomial 2x^{5}-5x-10 is not factored since it does not have any rational roots.

$$\frac{x^{3}\left(2x^{5}-5x-10\right)}{2}$$

Evaluate

$$x^{8}-\frac{5x^{4}}{2}-5x^{3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{8}-5x^{3} times \frac{2}{2}.

$$\frac{2\left(x^{8}-5x^{3}\right)}{2}-\frac{5x^{4}}{2}$$

Since \frac{2\left(x^{8}-5x^{3}\right)}{2} and \frac{5x^{4}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(x^{8}-5x^{3}\right)-5x^{4}}{2}$$

Do the multiplications in 2\left(x^{8}-5x^{3}\right)-5x^{4}.

$$\frac{2x^{8}-10x^{3}-5x^{4}}{2}$$