Solve x^3-2x^2-11x+12:x:4

$$x ^ { 3 } - 2 x ^ { 2 } - 11 x + 12 : x : 4$$

Evaluate

$$x^{3}-2x^{2}-11x+\frac{3}{x}$$

Short Solution Steps

Express \frac{\frac{12}{x}}{4} as a single fraction.

$$x^{3}-2x^{2}-11x+\frac{12}{x\times 4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3}-2x^{2}-11x times \frac{x\times 4}{x\times 4}.

$$\frac{\left(x^{3}-2x^{2}-11x\right)x\times 4}{x\times 4}+\frac{12}{x\times 4}$$

Since \frac{\left(x^{3}-2x^{2}-11x\right)x\times 4}{x\times 4} and \frac{12}{x\times 4} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{3}-2x^{2}-11x\right)x\times 4+12}{x\times 4}$$

Do the multiplications in \left(x^{3}-2x^{2}-11x\right)x\times 4+12.

$$\frac{4x^{4}-8x^{3}-44x^{2}+12}{x\times 4}$$

Factor the expressions that are not already factored in \frac{4x^{4}-8x^{3}-44x^{2}+12}{x\times 4}.

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

Cancel out 4 in both numerator and denominator.

$$\frac{x^{4}-2x^{3}-11x^{2}+3}{x}$$

Factor

$$\frac{x^{4}-2x^{3}-11x^{2}+3}{x}$$