Solve {l}{text{5.}2y^2-9y-18}{quad(y-6)(2y+3)}

$$\left. \begin{array} { l } { \text { 5. } 2 y ^ { 2 } - 9 y - 18 } \\ { \quad ( y - 6 ) ( 2 y + 3 ) } \end{array} \right.$$

Least Common Multiple

$$\left(y-6\right)\left(2y+3\right)\left(10y^{2}-9y-18\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$10y^{2}-9y-18=10\left(y-\left(-\frac{3}{20}\sqrt{89}+\frac{9}{20}\right)\right)\left(y-\left(\frac{3}{20}\sqrt{89}+\frac{9}{20}\right)\right)$$

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

$$10\left(y-6\right)\left(2y+3\right)\left(y-\frac{9-3\sqrt{89}}{20}\right)\left(y-\frac{3\sqrt{89}+9}{20}\right)$$

Expand the expression.

$$20y^{4}-108y^{3}-135y^{2}+324y+324$$

Evaluate

$$10y^{2}-9y-18,\ \left(y-6\right)\left(2y+3\right)$$