Solve x^4-2x^3-12x^2+70-20divx^2+3x-2

$$x ^ { 4 } - 2 x ^ { 3 } - 12 x ^ { 2 } + 70 - 20 \div x ^ { 2 } + 3 x - 2$$

Evaluate

$$x^{4}-2x^{3}-12x^{2}+3x+68-\frac{20}{x^{2}}$$

Short Solution Steps

Subtract 2 from 70 to get 68.

$$x^{4}-2x^{3}-12x^{2}+68-\frac{20}{x^{2}}+3x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{4}-2x^{3}-12x^{2}+68+3x times \frac{x^{2}}{x^{2}}.

$$\frac{\left(x^{4}-2x^{3}-12x^{2}+68+3x\right)x^{2}}{x^{2}}-\frac{20}{x^{2}}$$

Since \frac{\left(x^{4}-2x^{3}-12x^{2}+68+3x\right)x^{2}}{x^{2}} and \frac{20}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x^{4}-2x^{3}-12x^{2}+68+3x\right)x^{2}-20}{x^{2}}$$

Do the multiplications in \left(x^{4}-2x^{3}-12x^{2}+68+3x\right)x^{2}-20.

$$\frac{x^{6}-2x^{5}-12x^{4}+68x^{2}+3x^{3}-20}{x^{2}}$$

Factor

$$\frac{x^{6}-2x^{5}-12x^{4}+3x^{3}+68x^{2}-20}{x^{2}}$$