Solve 9x-6x^2+4x^3/3

$$9 x - 6 x ^ { 2 } + \frac { 4 x ^ { 3 } } { 3 }$$

Evaluate

$$\frac{4x^{3}}{3}-6x^{2}+9x$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 9x-6x^{2} times \frac{3}{3}.

$$\frac{3\left(9x-6x^{2}\right)}{3}+\frac{4x^{3}}{3}$$

Since \frac{3\left(9x-6x^{2}\right)}{3} and \frac{4x^{3}}{3} have the same denominator, add them by adding their numerators.

$$\frac{3\left(9x-6x^{2}\right)+4x^{3}}{3}$$

Do the multiplications in 3\left(9x-6x^{2}\right)+4x^{3}.

$$\frac{27x-18x^{2}+4x^{3}}{3}$$

Factor

$$\frac{x\left(4x^{2}-18x+27\right)}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{27x-18x^{2}+4x^{3}}{3}$$

Consider 27x-18x^{2}+4x^{3}. Factor out x.

$$x\left(27-18x+4x^{2}\right)$$

Rewrite the complete factored expression. Polynomial 27-18x+4x^{2} is not factored since it does not have any rational roots.

$$\frac{x\left(27-18x+4x^{2}\right)}{3}$$