Solve {l}{2x^2-16x-28}{9x^2-54x+36}

$$\left. \begin{array} { l } { 2 x ^ { 2 } - 16 x - 28 } \\ { 9 x ^ { 2 } - 54 x + 36 } \end{array} \right.$$

Least Common Multiple

$$18\left(\left(x-4\right)^{2}-30\right)\left(\left(x-3\right)^{2}-5\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$2x^{2}-16x-28=2\left(x-\left(\sqrt{30}+4\right)\right)\left(x-\left(-\sqrt{30}+4\right)\right) 9x^{2}-54x+36=9\left(x-\left(\sqrt{5}+3\right)\right)\left(x-\left(-\sqrt{5}+3\right)\right)$$

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

$$18\left(x-\left(3-\sqrt{5}\right)\right)\left(x-\left(4-\sqrt{30}\right)\right)\left(x-\left(\sqrt{5}+3\right)\right)\left(x-\left(\sqrt{30}+4\right)\right)$$

Expand the expression.

$$18x^{4}-252x^{3}+684x^{2}+936x-1008$$

Evaluate

$$2\left(x^{2}-8x-14\right),\ 9\left(x^{2}-6x+4\right)$$