Solve x^2-x-3,x^2-3x+6,x^2+2x+2

$$x ^ { 2 } - x - 3 , x ^ { 2 } - 3 x + 6 , x ^ { 2 } + 2 x + 2$$

Least Common Multiple

$$\frac{\left(x^{2}-3x+6\right)\left(x^{2}+2x+2\right)\left(\left(2x-1\right)^{2}-13\right)}{4}$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{2}-x-3=\left(x-\left(-\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)$$

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$\left(x-\frac{1-\sqrt{13}}{2}\right)\left(x-\frac{\sqrt{13}+1}{2}\right)\left(x^{2}-3x+6\right)\left(x^{2}+2x+2\right)$$

Expand the expression.

$$x^{6}-2x^{5}+7x^{3}-30x-36$$

Evaluate

$$x^{2}-x-3,x^{2}-3x+6,x^{2}+2x+2$$