Solve x^3+2x^2+4x+3divx^3+x+3

$${ x }^{ 3 } +2 { x }^{ 2 } +4x+3 \div { x }^{ 3 } +x+3$$

Evaluate

$$x^{3}+2x^{2}+5x+3+\frac{3}{x^{3}}$$

Short Solution Steps

Combine 4x and x to get 5x.

$$x^{3}+2x^{2}+5x+\frac{3}{x^{3}}+3$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3}+2x^{2}+5x+3 times \frac{x^{3}}{x^{3}}.

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

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

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

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

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

Factor

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