Solve {l}{2x^2-3x+16}{3x^2+6x-20}

$$\left. \begin{array} { l } { 2 x ^ { 2 } - 3 x + 16 } \\ { 3 x ^ { 2 } + 6 x - 20 } \end{array} \right.$$

Least Common Multiple

$$\frac{\left(2x^{2}-3x+16\right)\left(\left(3x+3\right)^{2}-69\right)}{3}$$

Solution Steps

Factor the expressions that are not already factored.

$$3x^{2}+6x-20=3\left(x-\left(-\frac{1}{3}\sqrt{69}-1\right)\right)\left(x-\left(\frac{1}{3}\sqrt{69}-1\right)\right)$$

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

$$3\left(x-\left(-\frac{\sqrt{69}}{3}-1\right)\right)\left(x-\left(\frac{\sqrt{69}}{3}-1\right)\right)\left(2x^{2}-3x+16\right)$$

Expand the expression.

$$6x^{4}+3x^{3}-10x^{2}+156x-320$$

Evaluate

$$2x^{2}-3x+16,\ 3x^{2}+6x-20$$