Solve {l}{4x^3-25}{x^3-3x^2-4x+12}

$$\left. \begin{array} { l } { 4 x ^ { 3 } - 25 } \\ { x ^ { 3 } - 3 x ^ { 2 } - 4 x + 12 } \end{array} \right.$$

Least Common Multiple

$$\left(x-3\right)\left(x^{2}-4\right)\left(4x^{3}-25\right)$$

Solution Steps

Factor the expressions that are not already factored.

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

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

$$\left(x-3\right)\left(x-2\right)\left(x+2\right)\left(4x^{3}-25\right)$$

Expand the expression.

$$4x^{6}-12x^{5}-16x^{4}+23x^{3}+75x^{2}+100x-300$$

Evaluate

$$4x^{3}-25,\ \left(x-3\right)\left(x^{2}-4\right)$$