Solve 2x^3-3x^2-4x+5div(x+3)

$$2 { x }^{ 3 } -3 { x }^{ 2 } -4x+5 \div (x+3)$$

Evaluate

$$\frac{2x^{4}+3x^{3}-13x^{2}-12x+5}{x+3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{3}-3x^{2}-4x times \frac{x+3}{x+3}.

$$\frac{\left(2x^{3}-3x^{2}-4x\right)\left(x+3\right)}{x+3}+\frac{5}{x+3}$$

Since \frac{\left(2x^{3}-3x^{2}-4x\right)\left(x+3\right)}{x+3} and \frac{5}{x+3} have the same denominator, add them by adding their numerators.

$$\frac{\left(2x^{3}-3x^{2}-4x\right)\left(x+3\right)+5}{x+3}$$

Do the multiplications in \left(2x^{3}-3x^{2}-4x\right)\left(x+3\right)+5.

$$\frac{2x^{4}+6x^{3}-3x^{3}-9x^{2}-4x^{2}-12x+5}{x+3}$$

Combine like terms in 2x^{4}+6x^{3}-3x^{3}-9x^{2}-4x^{2}-12x+5.

$$\frac{2x^{4}+3x^{3}-13x^{2}-12x+5}{x+3}$$

Differentiate w.r.t. x

$$\frac{6x^{4}+30x^{3}+14x^{2}-78x-41}{\left(x+3\right)^{2}}$$