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

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

Factor

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

Solution Steps

Factor out x.

$$x\left(-x^{2}+2x-1\right)$$

Consider -x^{2}+2x-1. Factor the expression by grouping. First, the expression needs to be rewritten as -x^{2}+ax+bx-1. To find a and b, set up a system to be solved.

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

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution.

$$a=1 b=1$$

Rewrite -x^{2}+2x-1 as \left(-x^{2}+x\right)+\left(x-1\right).

$$\left(-x^{2}+x\right)+\left(x-1\right)$$

Factor out -x in -x^{2}+x.

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

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

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

Rewrite the complete factored expression.

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

Evaluate

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