Solve {c}{x^3-112x^2-x+312-2x}{112x^2-112}

$$\left. \begin{array} { c } { x ^ { 3 } - 112 x ^ { 2 } - x + 312 - 2 x } \\ { 112 x ^ { 2 } - 112 } \end{array} \right.$$

Least Common Multiple

$$112\left(x^{2}-1\right)\left(x^{3}-112x^{2}-3x+312\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$112x^{2}-112=112\left(x-1\right)\left(x+1\right)$$

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

$$112\left(x-1\right)\left(x+1\right)\left(x^{3}-112x^{2}-3x+312\right)$$

Expand the expression.

$$112x^{5}-12544x^{4}-448x^{3}+47488x^{2}+336x-34944$$

Evaluate

$$x^{3}-112x^{2}-3x+312,\ 112\left(x^{2}-1\right)$$