Solve 4x^3+3x^2-16x-12div(x+2)

$$4 { x }^{ 3 } +3 { x }^{ 2 } -16x-12 \div (x+2)$$

Evaluate

$$\frac{4x^{4}+11x^{3}-10x^{2}-32x-12}{x+2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4x^{3}+3x^{2}-16x times \frac{x+2}{x+2}.

$$\frac{\left(4x^{3}+3x^{2}-16x\right)\left(x+2\right)}{x+2}-\frac{12}{x+2}$$

Since \frac{\left(4x^{3}+3x^{2}-16x\right)\left(x+2\right)}{x+2} and \frac{12}{x+2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(4x^{3}+3x^{2}-16x\right)\left(x+2\right)-12}{x+2}$$

Do the multiplications in \left(4x^{3}+3x^{2}-16x\right)\left(x+2\right)-12.

$$\frac{4x^{4}+8x^{3}+3x^{3}+6x^{2}-16x^{2}-32x-12}{x+2}$$

Combine like terms in 4x^{4}+8x^{3}+3x^{3}+6x^{2}-16x^{2}-32x-12.

$$\frac{4x^{4}+11x^{3}-10x^{2}-32x-12}{x+2}$$

Differentiate w.r.t. x

$$\frac{2\left(6x^{4}+27x^{3}+28x^{2}-20x-26\right)}{\left(x+2\right)^{2}}$$