Solve -1-1/2x-1/6x^3-1/2x^2-1/2x-frac{x^3}{6}-frac{x^2}{2}+x+1

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

Combine -x and x to get 0.

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

Add -1 and 1 to get 0.

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

Factor

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

Solution Steps

Factor out \frac{1}{6}.

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

Consider -6-3x-x^{3}-3x^{2}-3x-x^{3}-3x^{2}+6x+6. Multiply and combine like terms.

$$-2x^{3}-6x^{2}$$

Consider -2x^{3}-6x^{2}. Factor out 2.

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

Consider -x^{3}-3x^{2}. Factor out x^{2}.

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

Rewrite the complete factored expression.

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

Simplify.

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