Solve x^4/4-x^3/2+x

$$\frac{ { x }^{ 4 } }{ 4 } - \frac{ { x }^{ 3 } }{ 2 } +x$$

Factor

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

Solution Steps

Factor out \frac{1}{4}.

$$\frac{x^{4}-2x^{3}+4x}{4}$$

Consider x^{4}-2x^{3}+4x. Factor out x.

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

Rewrite the complete factored expression. Polynomial x^{3}-2x^{2}+4 is not factored since it does not have any rational roots.

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

Evaluate

$$\frac{x^{4}}{4}-\frac{x^{3}}{2}+x$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{x^{3}}{2} times \frac{2}{2}.

$$\frac{x^{4}}{4}-\frac{2x^{3}}{4}+x$$

Since \frac{x^{4}}{4} and \frac{2x^{3}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{4}-2x^{3}}{4}+x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{4}{4}.

$$\frac{x^{4}-2x^{3}}{4}+\frac{4x}{4}$$

Since \frac{x^{4}-2x^{3}}{4} and \frac{4x}{4} have the same denominator, add them by adding their numerators.

$$\frac{x^{4}-2x^{3}+4x}{4}$$