Solve 12x^3+8x^2-4x

$$12 x ^ { 3 } + 8 x ^ { 2 } - 4 x$$

Factor

$$4x\left(3x-1\right)\left(x+1\right)$$

Solution Steps

Factor out 4.

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

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

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

Consider 3x^{2}+2x-1. Factor the expression by grouping. First, the expression needs to be rewritten as 3x^{2}+ax+bx-1. To find a and b, set up a system to be solved.

$$a+b=2 ab=3\left(-1\right)=-3$$

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.

$$a=-1 b=3$$

Rewrite 3x^{2}+2x-1 as \left(3x^{2}-x\right)+\left(3x-1\right).

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

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

$$x\left(3x-1\right)+3x-1$$

Factor out common term 3x-1 by using distributive property.

$$\left(3x-1\right)\left(x+1\right)$$

Rewrite the complete factored expression.

$$4x\left(3x-1\right)\left(x+1\right)$$

Evaluate

$$4x\left(3x-1\right)\left(x+1\right)$$