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

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

Calcular

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

Pasos da solución

Combina -\frac{1}{2}x e -\frac{1}{2}x para obter -x.

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

Combina -\frac{1}{6}x^{3} e -\frac{x^{3}}{6} para obter -\frac{1}{3}x^{3}.

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

Combina -\frac{1}{2}x^{2} e -\frac{x^{2}}{2} para obter -x^{2}.

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

Combina -x e x para obter 0.

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

Suma -1 e 1 para obter 0.

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

Factorizar

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

Pasos da solución

Factoriza \frac{1}{6}.

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

Considera -6-3x-x^{3}-3x^{2}-3x-x^{3}-3x^{2}+6x+6. Multiplica e combina termos semellantes.

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

Considera -2x^{3}-6x^{2}. Factoriza 2.

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

Considera -x^{3}-3x^{2}. Factoriza x^{2}.

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

Reescribe a expresión factorizada completa.

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

Simplifica.

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