Solve x^{3}-1,x^{3}-x^2+x^7x^4+x^2+1

$$x ^ { 3 } - 1 , x ^ { 3 } - x ^ { 2 } + x ^ { 7 } x ^ { 4 } + x ^ { 2 } + 1$$

Least Common Multiple

$$\left(x^{3}-1\right)\left(x^{11}+x^{3}+1\right)$$

Solution Steps

Factor the expressions that are not already factored.

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

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

$$\left(x-1\right)\left(x^{2}+x+1\right)\left(x^{11}+x^{3}+1\right)$$

Expand the expression.

$$x^{14}-x^{11}+x^{6}-1$$

Evaluate

$$x^{3}-1,x^{11}+x^{3}+1$$