Solve x^3+2x^2-6x+1div(x+2)

$${ x }^{ 3 } +2 { x }^{ 2 } -6x+1 \div (x+2)$$

Evaluate

$$\frac{x^{4}+4x^{3}-2x^{2}-12x+1}{x+2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3}+2x^{2}-6x times \frac{x+2}{x+2}.

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

Since \frac{\left(x^{3}+2x^{2}-6x\right)\left(x+2\right)}{x+2} and \frac{1}{x+2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(x^{3}+2x^{2}-6x\right)\left(x+2\right)+1.

$$\frac{x^{4}+2x^{3}+2x^{3}+4x^{2}-6x^{2}-12x+1}{x+2}$$

Combine like terms in x^{4}+2x^{3}+2x^{3}+4x^{2}-6x^{2}-12x+1.

$$\frac{x^{4}+4x^{3}-2x^{2}-12x+1}{x+2}$$

Differentiate w.r.t. x

$$\frac{3x^{4}+16x^{3}+22x^{2}-8x-25}{\left(x+2\right)^{2}}$$