Solve {l}{x^{4}-5x^2+4}{3x^4-x^3-73x^2}

$$\left. \begin{array} { l } { x ^ { 4 } - 5 x ^ { 2 } + 4 } \\ { 3 x ^ { 4 } - x ^ { 3 } - 73 x ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$x^{2}\left(x^{2}-4\right)\left(x^{2}-1\right)\left(3x^{2}-x-73\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{4}-5x^{2}+4=\left(x-2\right)\left(x-1\right)\left(x+1\right)\left(x+2\right) x^{2}\left(3x^{2}-x-73\right)=3\left(x-\left(-\frac{1}{6}\sqrt{877}+\frac{1}{6}\right)\right)\left(x-\left(\frac{1}{6}\sqrt{877}+\frac{1}{6}\right)\right)x^{2}$$

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

$$\left(x-2\right)\left(x-1\right)\left(x+1\right)\left(x+2\right)x^{2}\left(3x^{2}-x-73\right)$$

Expand the expression.

$$3x^{8}-x^{7}-88x^{6}+5x^{5}+377x^{4}-4x^{3}-292x^{2}$$

Evaluate

$$x^{4}-5x^{2}+4,\ x^{2}\left(3x^{2}-x-73\right)$$