Solve {l}{x^2+y-11}{x^2+x-10}

$$\left. \begin{array} { l } { x ^ { 2 } + y - 11 } \\ { x ^ { 2 } + x - 10 } \end{array} \right.$$

Least Common Multiple

$$\left(x^{2}+x-10\right)\left(x^{2}+y-11\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{2}+x-10=\left(x-\left(-\frac{1}{2}\sqrt{41}-\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{41}-\frac{1}{2}\right)\right)$$

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

$$\left(x^{2}+x-10\right)\left(x^{2}+y-11\right)$$

Expand the expression.

$$x^{4}+x^{3}-21x^{2}+xy-11x+yx^{2}-10y+110$$

Evaluate

$$x^{2}+y-11,\ x^{2}+x-10$$