Solve 8x^2-4x^3-4x

$$8 x ^ { 2 } - 4 x ^ { 3 } - 4 x$$

Factor

$$-4x\left(1-x\right)^{2}$$

Solution Steps

Factor out 4.

$$4\left(2x^{2}-x^{3}-x\right)$$

Consider 2x^{2}-x^{3}-x. Factor out x.

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

Consider 2x-x^{2}-1. Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.

$$-x^{2}+2x-1$$

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.

$$4x\left(x-1\right)\left(-x+1\right)$$

Evaluate

$$-4x\left(1-x\right)^{2}$$