Solve f(2)=x^3-3x^2/2-6x

$$f ( 2 ) = x ^ { 3 } - \frac { 3 x ^ { 2 } } { 2 } - 6 x$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3}-6x times \frac{2}{2}.

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

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

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

Do the multiplications in 2\left(x^{3}-6x\right)-3x^{2}.

$$\frac{2x^{3}-12x-3x^{2}}{2}$$

Divide each term of 2x^{3}-12x-3x^{2} by 2 to get -6x-\frac{3}{2}x^{2}+x^{3}.

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

Factor

$$x\left(x-\frac{3-\sqrt{105}}{4}\right)\left(x-\frac{\sqrt{105}+3}{4}\right)$$