Solve {l}{x^2+10x+21}{x^2-28x+96}{x^2-64}

$$\left. \begin{array} { l } { x ^ { 2 } + 10 x + 21 } \\ { x ^ { 2 } - 28 x + 96 } \\ { x ^ { 2 } - 64 } \end{array} \right.$$

Least Common Multiple

$$\left(x-24\right)\left(x-4\right)\left(x+3\right)\left(x+7\right)\left(x^{2}-64\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{2}-64=\left(x-8\right)\left(x+8\right)$$

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

$$\left(x-24\right)\left(x-8\right)\left(x-4\right)\left(x+3\right)\left(x+7\right)\left(x+8\right)$$

Expand the expression.

$$x^{6}-18x^{5}-227x^{4}+1524x^{3}+12448x^{2}-23808x-129024$$

Evaluate

$$\left(x+3\right)\left(x+7\right),\ \left(x-24\right)\left(x-4\right),\ x^{2}-64$$