Solve {l}{-3y^2+3y+24}{y^2+5y}

$$\left. \begin{array} { l } { - 3 y ^ { 2 } + 3 y + 24 } \\ { y ^ { 2 } + 5 y } \end{array} \right.$$

Least Common Multiple

$$3y\left(y+5\right)\left(y^{2}-y-8\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$-3y^{2}+3y+24=-3\left(y-\left(-\frac{1}{2}\sqrt{33}+\frac{1}{2}\right)\right)\left(y-\left(\frac{1}{2}\sqrt{33}+\frac{1}{2}\right)\right)$$

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

$$3y\left(y+5\right)\left(y^{2}-y-8\right)$$

Expand the expression.

$$3y^{4}+12y^{3}-39y^{2}-120y$$

Evaluate

$$3\left(8+y-y^{2}\right),\ y\left(y+5\right)$$