Solve f(x)=1/2x^3-3/xx^2-2x

$$f ( x ) = \frac { 1 } { 2 } x ^ { 3 } - \frac { 3 } { x } x ^ { 2 } - 2 x$$

Evaluate

$$\frac{x^{3}}{2}-5x$$

Solution Steps

Express \frac{3}{x}x^{2} as a single fraction.

$$\frac{1}{2}x^{3}-\frac{3x^{2}}{x}-2x$$

Cancel out x in both numerator and denominator.

$$\frac{1}{2}x^{3}-3x-2x$$

Combine -3x and -2x to get -5x.

$$\frac{1}{2}x^{3}-5x$$

Factor

$$\frac{x\left(x^{2}-10\right)}{2}$$

Solution Steps

Express \frac{3}{x}x^{2} as a single fraction.

$$factor(\frac{1}{2}x^{3}-\frac{3x^{2}}{x}-2x)$$

Cancel out x in both numerator and denominator.

$$factor(\frac{1}{2}x^{3}-3x-2x)$$

Combine -3x and -2x to get -5x.

$$factor(\frac{1}{2}x^{3}-5x)$$

Factor out \frac{1}{2}.

$$\frac{x^{3}-10x}{2}$$

Consider x^{3}-10x. Factor out x.

$$x\left(x^{2}-10\right)$$

Rewrite the complete factored expression. Polynomial x^{2}-10 is not factored since it does not have any rational roots.

$$\frac{x\left(x^{2}-10\right)}{2}$$