Solve x^4/4+x^2=

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

Evaluate

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

Solution Steps

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

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

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

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

Factor

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

Solution Steps

Factor out \frac{1}{4}.

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

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

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

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

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