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

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

Evaluate

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

Short Solution Steps

Express 2\times \frac{x^{3}}{3} as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply -3x^{2}+2x+4 times \frac{3}{3}.

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

Since \frac{2x^{3}}{3} and \frac{3\left(-3x^{2}+2x+4\right)}{3} have the same denominator, add them by adding their numerators.

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

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

$$\frac{2x^{3}-9x^{2}+6x+12}{3}$$

Factor

$$\frac{2x^{3}-9x^{2}+6x+12}{3}$$

Solution Steps

Factor out \frac{1}{3}. Polynomial 2x^{3}-9x^{2}+6x+12 is not factored since it does not have any rational roots.

$$\frac{2x^{3}-9x^{2}+6x+12}{3}$$