Solve f(x)=3x^2+x/2

$$f ( x ) = 3 x ^ { 2 } + \frac { x } { 2 }$$

Evaluate

$$\frac{x\left(6x+1\right)}{2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x^{2} times \frac{2}{2}.

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

Since \frac{2\times 3x^{2}}{2} and \frac{x}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\times 3x^{2}+x.

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

Factor

$$\frac{x\left(6x+1\right)}{2}$$

Solution Steps

Factor out \frac{1}{2}.

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

Consider 6x^{2}+x. Factor out x.

$$x\left(6x+1\right)$$

Rewrite the complete factored expression.

$$\frac{x\left(6x+1\right)}{2}$$