Solve {l}{(x-1)(x+2x^2-4x-10)}{(1)quad1+2-4-10}

$$\left. \begin{array} { l } { ( x - 1 ) ( x + 2 x ^ { 2 } - 4 x - 10 ) } \\ { ( 1 ) \quad 1 + 2 - 4 - 10 } \end{array} \right.$$

Least Common Multiple

$$11\left(x-1\right)\left(2x^{2}-3x-10\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$\left(x-1\right)\left(-3x+2x^{2}-10\right)=2\left(x-1\right)\left(x-\left(-\frac{1}{4}\sqrt{89}+\frac{3}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{89}+\frac{3}{4}\right)\right) -11=-11$$

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

$$22\left(x-1\right)\left(x-\frac{3-\sqrt{89}}{4}\right)\left(x-\frac{\sqrt{89}+3}{4}\right)$$

Expand the expression.

$$22x^{3}-55x^{2}-77x+110$$

Evaluate

$$\left(x-1\right)\left(2x^{2}-3x-10\right),\ -11$$