Solve x^3+x^40/200

$$x ^ { 3 } + \frac { x ^ { 40 } } { 200 }$$

Evaluate

$$\frac{x^{40}}{200}+x^{3}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3} times \frac{200}{200}.

$$\frac{200x^{3}}{200}+\frac{x^{40}}{200}$$

Since \frac{200x^{3}}{200} and \frac{x^{40}}{200} have the same denominator, add them by adding their numerators.

$$\frac{200x^{3}+x^{40}}{200}$$

Factor

$$\frac{x^{3}\left(x^{37}+200\right)}{200}$$

Solution Steps

Factor out \frac{1}{200}.

$$\frac{200x^{3}+x^{40}}{200}$$

Consider 200x^{3}+x^{40}. Factor out x^{3}.

$$x^{3}\left(200+x^{37}\right)$$

Rewrite the complete factored expression. Polynomial 200+x^{37} is not factored since it does not have any rational roots.

$$\frac{x^{3}\left(200+x^{37}\right)}{200}$$