Solve x^6/6-2x^4+8x^2-315

$$\frac { x ^ { 6 } } { 6 } - 2 x ^ { 4 } + 8 x ^ { 2 } - 315$$

Evaluate

$$\frac{x^{6}}{6}-2x^{4}+8x^{2}-315$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply -2x^{4}+8x^{2}-315 times \frac{6}{6}.

$$\frac{x^{6}}{6}+\frac{6\left(-2x^{4}+8x^{2}-315\right)}{6}$$

Since \frac{x^{6}}{6} and \frac{6\left(-2x^{4}+8x^{2}-315\right)}{6} have the same denominator, add them by adding their numerators.

$$\frac{x^{6}+6\left(-2x^{4}+8x^{2}-315\right)}{6}$$

Do the multiplications in x^{6}+6\left(-2x^{4}+8x^{2}-315\right).

$$\frac{x^{6}-12x^{4}+48x^{2}-1890}{6}$$

Factor

$$\frac{x^{6}-12x^{4}+48x^{2}-1890}{6}$$

Solution Steps

Factor out \frac{1}{6}. Polynomial x^{6}-12x^{4}+48x^{2}-1890 is not factored since it does not have any rational roots.

$$\frac{x^{6}-12x^{4}+48x^{2}-1890}{6}$$