Solve x^4/10+x^2/2+x/4

$$\frac { x ^ { 4 } } { 10 } + \frac { x ^ { 2 } } { 2 } + \frac { x } { 4 }$$

Factor

$$\frac{x\left(2x^{3}+10x+5\right)}{20}$$

Solution Steps

Factor out \frac{1}{20}.

$$\frac{2x^{4}+10x^{2}+5x}{20}$$

Consider 2x^{4}+10x^{2}+5x. Factor out x.

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

Rewrite the complete factored expression. Polynomial 2x^{3}+10x+5 is not factored since it does not have any rational roots.

$$\frac{x\left(2x^{3}+10x+5\right)}{20}$$

Evaluate

$$\frac{x^{4}}{10}+\frac{x^{2}}{2}+\frac{x}{4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 2 is 10. Multiply \frac{x^{2}}{2} times \frac{5}{5}.

$$\frac{x^{4}}{10}+\frac{5x^{2}}{10}+\frac{x}{4}$$

Since \frac{x^{4}}{10} and \frac{5x^{2}}{10} have the same denominator, add them by adding their numerators.

$$\frac{x^{4}+5x^{2}}{10}+\frac{x}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 4 is 20. Multiply \frac{x^{4}+5x^{2}}{10} times \frac{2}{2}. Multiply \frac{x}{4} times \frac{5}{5}.

$$\frac{2\left(x^{4}+5x^{2}\right)}{20}+\frac{5x}{20}$$

Since \frac{2\left(x^{4}+5x^{2}\right)}{20} and \frac{5x}{20} have the same denominator, add them by adding their numerators.

$$\frac{2\left(x^{4}+5x^{2}\right)+5x}{20}$$

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

$$\frac{2x^{4}+10x^{2}+5x}{20}$$