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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Factor

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

Solution Steps

Factor out \frac{1}{2}.

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

Consider x^{3}-2x^{2}+6x. Factor out x.

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

Rewrite the complete factored expression. Polynomial x^{2}-2x+6 is not factored since it does not have any rational roots.

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