Solve {l}{-Xquad(2X-3)}{3Xquad(X^2-3X-1)}

$$\left. \begin{array} { l } { - X \quad ( 2 X - 3 ) } \\ { 3 X \quad ( X ^ { 2 } - 3 X - 1 ) } \end{array} \right.$$

Least Common Multiple

$$3X\left(2X-3\right)\left(X^{2}-3X-1\right)$$

Solution Steps

Factor the expressions that are not already factored.

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

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

$$3X\left(2X-3\right)\left(X^{2}-3X-1\right)$$

Expand the expression.

$$6X^{4}-27X^{3}+21X^{2}+9X$$

Evaluate

$$-X\left(2X-3\right),\ 3X\left(X^{2}-3X-1\right)$$