Solve -675x^2+x^4/2+3x^3+675x

$$-675 { x }^{ 2 } + \frac{ { x }^{ 4 } }{ 2 } +3 { x }^{ 3 } +675x$$

Evaluate

$$\frac{x\left(x^{3}+6x^{2}-1350x+1350\right)}{2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply -675x^{2}+3x^{3}+675x times \frac{2}{2}.

$$\frac{2\left(-675x^{2}+3x^{3}+675x\right)}{2}+\frac{x^{4}}{2}$$

Since \frac{2\left(-675x^{2}+3x^{3}+675x\right)}{2} and \frac{x^{4}}{2} have the same denominator, add them by adding their numerators.

$$\frac{2\left(-675x^{2}+3x^{3}+675x\right)+x^{4}}{2}$$

Do the multiplications in 2\left(-675x^{2}+3x^{3}+675x\right)+x^{4}.

$$\frac{-1350x^{2}+6x^{3}+1350x+x^{4}}{2}$$

Factor

$$\frac{x\left(x^{3}+6x^{2}-1350x+1350\right)}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{-1350x^{2}+x^{4}+6x^{3}+1350x}{2}$$

Consider -1350x^{2}+x^{4}+6x^{3}+1350x. Factor out x.

$$x\left(-1350x+x^{3}+6x^{2}+1350\right)$$

Rewrite the complete factored expression. Polynomial -1350x+x^{3}+6x^{2}+1350 is not factored since it does not have any rational roots.

$$\frac{x\left(-1350x+x^{3}+6x^{2}+1350\right)}{2}$$