Solve x^2-8,x^3+8,x^2-2x-8

$$x ^ { 2 } - 8 , x ^ { 3 } + 8 , x ^ { 2 } - 2 x - 8$$

Least Common Multiple

$$\left(x-4\right)\left(x^{2}-8\right)\left(x^{3}+8\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{3}+8=\left(x+2\right)\left(x^{2}-2x+4\right) -8-2x+x^{2}=\left(x-4\right)\left(x+2\right)$$

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

$$\left(x-4\right)\left(x+2\right)\left(x^{2}-8\right)\left(x^{2}-2x+4\right)$$

Expand the expression.

$$x^{6}-4x^{5}-8x^{4}+40x^{3}-32x^{2}-64x+256$$

Evaluate

$$x^{2}-8,x^{3}+8,\left(x-4\right)\left(x+2\right)$$