Solve {l}{text{1.}x^2+11x+30}{text{3.}x^2+20x-69}

$$\left. \begin{array} { l } { \text { 1. } x ^ { 2 } + 11 x + 30 } \\ { \text { 3. } x ^ { 2 } + 20 x - 69 } \end{array} \right.$$

Least Common Multiple

$$\left(x+5\right)\left(x+6\right)\left(3x^{2}+20x-69\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{2}+11x+30=\left(x+5\right)\left(x+6\right) 3x^{2}+20x-69=3\left(x-\left(-\frac{1}{3}\sqrt{307}-\frac{10}{3}\right)\right)\left(x-\left(\frac{1}{3}\sqrt{307}-\frac{10}{3}\right)\right)$$

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

$$3\left(x+5\right)\left(x+6\right)\left(x-\frac{-\sqrt{307}-10}{3}\right)\left(x-\frac{\sqrt{307}-10}{3}\right)$$

Expand the expression.

$$3x^{4}+53x^{3}+241x^{2}-159x-2070$$

Evaluate

$$x^{2}+11x+30,\ 3x^{2}+20x-69$$