Solve g(x)=1+x+x^2/2

$$g ( x ) = 1 + x + \frac { x ^ { 2 } } { 2 }$$

Evaluate

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

Short Solution Steps

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

$$\frac{2\left(1+x\right)}{2}+\frac{x^{2}}{2}$$

Since \frac{2\left(1+x\right)}{2} and \frac{x^{2}}{2} have the same denominator, add them by adding their numerators.

$$\frac{2\left(1+x\right)+x^{2}}{2}$$

Do the multiplications in 2\left(1+x\right)+x^{2}.

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

Factor

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

Solution Steps

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

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