Solve 2x^3-x^2+17x+17div(x-1)

$$2 { x }^{ 3 } - { x }^{ 2 } +17x+17 \div (x-1)$$

Evaluate

$$\frac{2x^{4}-3x^{3}+18x^{2}-17x+17}{x-1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{3}-x^{2}+17x times \frac{x-1}{x-1}.

$$\frac{\left(2x^{3}-x^{2}+17x\right)\left(x-1\right)}{x-1}+\frac{17}{x-1}$$

Since \frac{\left(2x^{3}-x^{2}+17x\right)\left(x-1\right)}{x-1} and \frac{17}{x-1} have the same denominator, add them by adding their numerators.

$$\frac{\left(2x^{3}-x^{2}+17x\right)\left(x-1\right)+17}{x-1}$$

Do the multiplications in \left(2x^{3}-x^{2}+17x\right)\left(x-1\right)+17.

$$\frac{2x^{4}-2x^{3}-x^{3}+x^{2}+17x^{2}-17x+17}{x-1}$$

Combine like terms in 2x^{4}-2x^{3}-x^{3}+x^{2}+17x^{2}-17x+17.

$$\frac{2x^{4}-3x^{3}+18x^{2}-17x+17}{x-1}$$

Differentiate w.r.t. x

$$\frac{x\left(6x^{3}-14x^{2}+27x-36\right)}{\left(x-1\right)^{2}}$$