Solve 2x^3+5x^2-10x+1divx^2-4

$$2 x ^ { 3 } + 5 x ^ { 2 } - 10 x + 1 \div x ^ { 2 } - 4$$

Evaluate

$$2x^{3}+5x^{2}-10x-4+\frac{1}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{3}+5x^{2}-10x-4 times \frac{x^{2}}{x^{2}}.

$$\frac{\left(2x^{3}+5x^{2}-10x-4\right)x^{2}}{x^{2}}+\frac{1}{x^{2}}$$

Since \frac{\left(2x^{3}+5x^{2}-10x-4\right)x^{2}}{x^{2}} and \frac{1}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(2x^{3}+5x^{2}-10x-4\right)x^{2}+1}{x^{2}}$$

Do the multiplications in \left(2x^{3}+5x^{2}-10x-4\right)x^{2}+1.

$$\frac{2x^{5}+5x^{4}-10x^{3}-4x^{2}+1}{x^{2}}$$

Factor

$$\frac{2x^{5}+5x^{4}-10x^{3}-4x^{2}+1}{x^{2}}$$