Solve x^3-7x^2-5x+2div(x-2)

$${ x }^{ 3 } -7 { x }^{ 2 } -5x+2 \div (x-2)$$

Evaluate

$$\frac{x^{4}-9x^{3}+9x^{2}+10x+2}{x-2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3}-7x^{2}-5x times \frac{x-2}{x-2}.

$$\frac{\left(x^{3}-7x^{2}-5x\right)\left(x-2\right)}{x-2}+\frac{2}{x-2}$$

Since \frac{\left(x^{3}-7x^{2}-5x\right)\left(x-2\right)}{x-2} and \frac{2}{x-2} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{3}-7x^{2}-5x\right)\left(x-2\right)+2}{x-2}$$

Do the multiplications in \left(x^{3}-7x^{2}-5x\right)\left(x-2\right)+2.

$$\frac{x^{4}-2x^{3}-7x^{3}+14x^{2}-5x^{2}+10x+2}{x-2}$$

Combine like terms in x^{4}-2x^{3}-7x^{3}+14x^{2}-5x^{2}+10x+2.

$$\frac{x^{4}-9x^{3}+9x^{2}+10x+2}{x-2}$$

Differentiate w.r.t. x

$$\frac{3x^{4}-26x^{3}+63x^{2}-36x-22}{\left(x-2\right)^{2}}$$