Solve 6-4x-5x^2/2+2x^3

$$6 - 4 x - \frac { 5 x ^ { 2 } } { 2 } + 2 x ^ { 3 }$$

Evaluate

$$2x^{3}-\frac{5x^{2}}{2}-4x+6$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 6-4x+2x^{3} times \frac{2}{2}.

$$\frac{2\left(6-4x+2x^{3}\right)}{2}-\frac{5x^{2}}{2}$$

Since \frac{2\left(6-4x+2x^{3}\right)}{2} and \frac{5x^{2}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(6-4x+2x^{3}\right)-5x^{2}}{2}$$

Do the multiplications in 2\left(6-4x+2x^{3}\right)-5x^{2}.

$$\frac{12-8x+4x^{3}-5x^{2}}{2}$$

Factor

$$\frac{4x^{3}-5x^{2}-8x+12}{2}$$

Solution Steps

Factor out \frac{1}{2}. Polynomial 12-8x-5x^{2}+4x^{3} is not factored since it does not have any rational roots.

$$\frac{12-8x-5x^{2}+4x^{3}}{2}$$