Solve f(x)=2x^5+x/3

$$f ( x ) = 2 x ^ { 5 } + \frac { x } { 3 }$$

Evaluate

$$2x^{5}+\frac{x}{3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{5} times \frac{3}{3}.

$$\frac{3\times 2x^{5}}{3}+\frac{x}{3}$$

Since \frac{3\times 2x^{5}}{3} and \frac{x}{3} have the same denominator, add them by adding their numerators.

$$\frac{3\times 2x^{5}+x}{3}$$

Do the multiplications in 3\times 2x^{5}+x.

$$\frac{6x^{5}+x}{3}$$

Factor

$$\frac{x\left(6x^{4}+1\right)}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{6x^{5}+x}{3}$$

Consider 6x^{5}+x. Factor out x.

$$x\left(6x^{4}+1\right)$$

Rewrite the complete factored expression. Polynomial 6x^{4}+1 is not factored since it does not have any rational roots.

$$\frac{x\left(6x^{4}+1\right)}{3}$$