Solve {l}{x^2+3x-10}{A}{B}{c}{x^2+10x-5}

$$\left. \begin{array} { l } { x ^ { 2 } + 3 x - 10 } \\ { A } \\ { B } \\ { c } \\ { x ^ { 2 } + 10 x - 5 } \end{array} \right.$$

Least Common Multiple

$$ABc\left(x-2\right)\left(x+5\right)\left(x^{2}+10x-5\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{2}+3x-10=\left(x-2\right)\left(x+5\right) x^{2}+10x-5=\left(x-\left(\sqrt{30}-5\right)\right)\left(x-\left(-\sqrt{30}-5\right)\right)$$

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

$$ABc\left(x-2\right)\left(x+5\right)\left(x^{2}+10x-5\right)$$

Expand the expression.

$$ABcx^{4}+13ABcx^{3}+15ABcx^{2}-115ABcx+50ABc$$

Evaluate

$$x^{2}+3x-10,\ A,\ B,\ c,\ x^{2}+10x-5$$