Solve 2/3x-1/6x^2+5x^3-1/3x^2-5/6x+3-2x^3

$$\frac { 2 } { 3 } x - \frac { 1 } { 6 } x ^ { 2 } + 5 x ^ { 3 } - \frac { 1 } { 3 } x ^ { 2 } - \frac { 5 } { 6 } x + 3 - 2 x ^ { 3 }$$

Evaluate

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

Solution Steps

Combine -\frac{1}{6}x^{2} and -\frac{1}{3}x^{2} to get -\frac{1}{2}x^{2}.

$$\frac{2}{3}x-\frac{1}{2}x^{2}+5x^{3}-\frac{5}{6}x+3-2x^{3}$$

Combine \frac{2}{3}x and -\frac{5}{6}x to get -\frac{1}{6}x.

$$-\frac{1}{6}x-\frac{1}{2}x^{2}+5x^{3}+3-2x^{3}$$

Combine 5x^{3} and -2x^{3} to get 3x^{3}.

$$-\frac{1}{6}x-\frac{1}{2}x^{2}+3x^{3}+3$$

Factor

$$\frac{18x^{3}-3x^{2}-x+18}{6}$$

Solution Steps

Factor out \frac{1}{6}. Polynomial 18x^{3}-3x^{2}-x+18 is not factored since it does not have any rational roots.

$$\frac{4x-x^{2}+30x^{3}-2x^{2}-5x+18-12x^{3}}{6}$$