Solve {l}{3x^2+4x+10}{-10x^2+3x+96}{1}

$$\left. \begin{array} { l } { 3 x ^ { 2 } + 4 x + 10 } \\ { - 10 x ^ { 2 } + 3 x + 96 } \\ { 1 } \end{array} \right.$$

Least Common Multiple

$$\frac{\left(3x^{2}+4x+10\right)\left(\left(20x-3\right)^{2}-3849\right)}{40}$$

Solution Steps

Factor the expressions that are not already factored.

$$-10x^{2}+3x+96=-10\left(x-\left(-\frac{1}{20}\sqrt{3849}+\frac{3}{20}\right)\right)\left(x-\left(\frac{1}{20}\sqrt{3849}+\frac{3}{20}\right)\right)$$

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

$$10\left(x-\frac{3-\sqrt{3849}}{20}\right)\left(x-\frac{\sqrt{3849}+3}{20}\right)\left(3x^{2}+4x+10\right)$$

Expand the expression.

$$30x^{4}+31x^{3}-200x^{2}-414x-960$$

Evaluate

$$3x^{2}+4x+10,\ 96+3x-10x^{2},\ 1$$