Solve -1+x/2+x^2/6+x^3/24

$$- 1 + \frac { x } { 2 } + \frac { x ^ { 2 } } { 6 } + \frac { x ^ { 3 } } { 24 }$$

Evaluate

$$\frac{x^{3}}{24}+\frac{x^{2}}{6}+\frac{x}{2}-1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply -1 times \frac{2}{2}.

$$-\frac{2}{2}+\frac{x}{2}+\frac{x^{2}}{6}+\frac{x^{3}}{24}$$

Since -\frac{2}{2} and \frac{x}{2} have the same denominator, add them by adding their numerators.

$$\frac{-2+x}{2}+\frac{x^{2}}{6}+\frac{x^{3}}{24}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 6 is 6. Multiply \frac{-2+x}{2} times \frac{3}{3}.

$$\frac{3\left(-2+x\right)}{6}+\frac{x^{2}}{6}+\frac{x^{3}}{24}$$

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

$$\frac{3\left(-2+x\right)+x^{2}}{6}+\frac{x^{3}}{24}$$

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

$$\frac{-6+3x+x^{2}}{6}+\frac{x^{3}}{24}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 24 is 24. Multiply \frac{-6+3x+x^{2}}{6} times \frac{4}{4}.

$$\frac{4\left(-6+3x+x^{2}\right)}{24}+\frac{x^{3}}{24}$$

Since \frac{4\left(-6+3x+x^{2}\right)}{24} and \frac{x^{3}}{24} have the same denominator, add them by adding their numerators.

$$\frac{4\left(-6+3x+x^{2}\right)+x^{3}}{24}$$

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

$$\frac{-24+12x+4x^{2}+x^{3}}{24}$$

Factor

$$\frac{x^{3}+4x^{2}+12x-24}{24}$$

Solution Steps

Factor out \frac{1}{24}. Polynomial -24+12x+4x^{2}+x^{3} is not factored since it does not have any rational roots.

$$\frac{-24+12x+4x^{2}+x^{3}}{24}$$