Solve x^2+x^3-2x=

$$x ^ { 2 } + x ^ { 3 } - 2 x =$$

Factor

$$x\left(x-1\right)\left(x+2\right)$$

Solution Steps

Factor out x.

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

Consider x+x^{2}-2. Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.

$$x^{2}+x-2$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-2. To find a and b, set up a system to be solved.

$$a+b=1 ab=1\left(-2\right)=-2$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. The only such pair is the system solution.

$$a=-1 b=2$$

Rewrite x^{2}+x-2 as \left(x^{2}-x\right)+\left(2x-2\right).

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

Factor out x in the first and 2 in the second group.

$$x\left(x-1\right)+2\left(x-1\right)$$

Factor out common term x-1 by using distributive property.

$$\left(x-1\right)\left(x+2\right)$$

Rewrite the complete factored expression.

$$x\left(x-1\right)\left(x+2\right)$$

Evaluate

$$x\left(x-1\right)\left(x+2\right)$$