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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

Differentiate w.r.t. x

$$\frac{3x^{4}+10x^{3}+11x^{2}+4x-1}{\left(x+1\right)^{2}}$$