Solve x^4+3x^3+10x/3+3x

$${ x }^{ 4 } +3 { x }^{ 3 } + \frac{ 10x }{ 3 } +3x$$

Evaluate

$$x^{4}+3x^{3}+\frac{19x}{3}$$

Short Solution Steps

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

$$\frac{3\left(x^{4}+3x^{3}+3x\right)}{3}+\frac{10x}{3}$$

Since \frac{3\left(x^{4}+3x^{3}+3x\right)}{3} and \frac{10x}{3} have the same denominator, add them by adding their numerators.

$$\frac{3\left(x^{4}+3x^{3}+3x\right)+10x}{3}$$

Do the multiplications in 3\left(x^{4}+3x^{3}+3x\right)+10x.

$$\frac{3x^{4}+9x^{3}+9x+10x}{3}$$

Combine like terms in 3x^{4}+9x^{3}+9x+10x.

$$\frac{3x^{4}+9x^{3}+19x}{3}$$

Factor

$$\frac{x\left(3x^{3}+9x^{2}+19\right)}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{3x^{4}+9x^{3}+10x+9x}{3}$$

Consider 3x^{4}+9x^{3}+10x+9x. Factor out x.

$$x\left(3x^{3}+9x^{2}+19\right)$$

Rewrite the complete factored expression. Polynomial 3x^{3}+9x^{2}+19 is not factored since it does not have any rational roots.

$$\frac{x\left(3x^{3}+9x^{2}+19\right)}{3}$$