Solve 4x^4-4x^3-13x+11x+4/2x^2+x-4

$$\frac { 4 x ^ { 4 } - 4 x ^ { 3 } - 13 x + 11 x + 4 } { 2 x ^ { 2 } + x - 4 }$$

Evaluate

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

Short Solution Steps

Combine -13x and 11x to get -2x.

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

Factor the expressions that are not already factored.

$$\frac{2\left(2x^{4}-2x^{3}-x+2\right)}{2\left(x-\left(-\frac{1}{4}\sqrt{33}-\frac{1}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{33}-\frac{1}{4}\right)\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2x^{4}-2x^{3}-x+2}{\left(x-\left(-\frac{1}{4}\sqrt{33}-\frac{1}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{33}-\frac{1}{4}\right)\right)}$$

Expand the expression.

$$\frac{2x^{4}-2x^{3}-x+2}{x^{2}+\frac{1}{2}x-2}$$

Expand

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

Short Solution Steps

Combine -13x and 11x to get -2x.

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

Factor the expressions that are not already factored.

$$\frac{2\left(2x^{4}-2x^{3}-x+2\right)}{2\left(x-\left(-\frac{1}{4}\sqrt{33}-\frac{1}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{33}-\frac{1}{4}\right)\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2x^{4}-2x^{3}-x+2}{\left(x-\left(-\frac{1}{4}\sqrt{33}-\frac{1}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{33}-\frac{1}{4}\right)\right)}$$

Expand the expression.

$$\frac{2x^{4}-2x^{3}-x+2}{x^{2}+\frac{1}{2}x-2}$$