Solve 5x^4-2x/3+6x

$$5 x ^ { 4 } - \frac { 2 x } { 3 } + 6 x$$

Evaluate

$$5x^{4}+\frac{16x}{3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5x^{4}+6x times \frac{3}{3}.

$$\frac{3\left(5x^{4}+6x\right)}{3}-\frac{2x}{3}$$

Since \frac{3\left(5x^{4}+6x\right)}{3} and \frac{2x}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(5x^{4}+6x\right)-2x}{3}$$

Do the multiplications in 3\left(5x^{4}+6x\right)-2x.

$$\frac{15x^{4}+18x-2x}{3}$$

Combine like terms in 15x^{4}+18x-2x.

$$\frac{15x^{4}+16x}{3}$$

Factor

$$\frac{x\left(15x^{3}+16\right)}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{15x^{4}-2x+18x}{3}$$

Consider 15x^{4}-2x+18x. Factor out x.

$$x\left(15x^{3}+16\right)$$

Rewrite the complete factored expression. Polynomial 15x^{3}+16 is not factored since it does not have any rational roots.

$$\frac{x\left(15x^{3}+16\right)}{3}$$