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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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}}{2} times \frac{3}{3}.

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

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

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

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

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

Factor

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

Solution Steps

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

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