Solve {r}{-6+11x^4+3x-2x^5}{6+3x-4x^2}

$$\left. \begin{array} { r } { - 6 + 11 x ^ { 4 } + 3 x - 2 x ^ { 5 } } \\ { 6 + 3 x - 4 x ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\frac{\left(\left(8x-3\right)^{2}-105\right)\left(2x^{5}-11x^{4}-3x+6\right)}{16}$$

Solution Steps

Factor the expressions that are not already factored.

$$6+3x-4x^{2}=-4\left(x-\left(-\frac{1}{8}\sqrt{105}+\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{105}+\frac{3}{8}\right)\right)$$

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

$$4\left(x-\frac{3-\sqrt{105}}{8}\right)\left(x-\frac{\sqrt{105}+3}{8}\right)\left(2x^{5}-11x^{4}-3x+6\right)$$

Expand the expression.

$$8x^{7}-50x^{6}+21x^{5}+66x^{4}-12x^{3}+33x^{2}-36$$

Evaluate

$$-2x^{5}+11x^{4}+3x-6,\ 6+3x-4x^{2}$$