Solve {l}{x^2-3x+2x}{x^3+5x^6-2}

$$\left. \begin{array} { l } { x ^ { 2 } - 3 x + 2 x } \\ { x ^ { 3 } + 5 x ^ { 6 } - 2 } \end{array} \right.$$

Least Common Multiple

$$x\left(x-1\right)\left(5x^{6}+x^{3}-2\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{3}+5x^{6}-2=5\left(x^{3}-\left(-\frac{1}{10}\sqrt{41}-\frac{1}{10}\right)\right)\left(x^{3}-\left(\frac{1}{10}\sqrt{41}-\frac{1}{10}\right)\right)$$

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

$$x\left(x-1\right)\left(5x^{6}+x^{3}-2\right)$$

Expand the expression.

$$5x^{8}-5x^{7}+x^{5}-x^{4}-2x^{2}+2x$$

Evaluate

$$x\left(x-1\right),\ 5x^{6}+x^{3}-2$$