Solve c-3x^3+11x^2-20div(x-2)

$$c - 3 x ^ { 3 } + 11 x ^ { 2 } - 20 \div ( x - 2 )$$

Evaluate

$$\frac{-3x^{4}+17x^{3}-22x^{2}+cx-2c-20}{x-2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply c-3x^{3}+11x^{2} times \frac{x-2}{x-2}.

$$\frac{\left(c-3x^{3}+11x^{2}\right)\left(x-2\right)}{x-2}-\frac{20}{x-2}$$

Since \frac{\left(c-3x^{3}+11x^{2}\right)\left(x-2\right)}{x-2} and \frac{20}{x-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(c-3x^{3}+11x^{2}\right)\left(x-2\right)-20}{x-2}$$

Do the multiplications in \left(c-3x^{3}+11x^{2}\right)\left(x-2\right)-20.

$$\frac{cx-2c-3x^{4}+6x^{3}+11x^{3}-22x^{2}-20}{x-2}$$

Combine like terms in cx-2c-3x^{4}+6x^{3}+11x^{3}-22x^{2}-20.

$$\frac{-22x^{2}+cx+17x^{3}-2c-3x^{4}-20}{x-2}$$

Differentiate w.r.t. x

$$\frac{20+88x-124x^{2}+58x^{3}-9x^{4}}{\left(x-2\right)^{2}}$$