Solve 2x^3-10x^2-12x

$$2 x ^ { 3 } - 10 x ^ { 2 } - 12 x$$

Factor

$$2x\left(x-6\right)\left(x+1\right)$$

Solution Steps

Factor out 2.

$$2\left(x^{3}-5x^{2}-6x\right)$$

Consider x^{3}-5x^{2}-6x. Factor out x.

$$x\left(x^{2}-5x-6\right)$$

Consider x^{2}-5x-6. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-6. To find a and b, set up a system to be solved.

$$a+b=-5 ab=1\left(-6\right)=-6$$

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -6.

$$1,-6 2,-3$$

Calculate the sum for each pair.

$$1-6=-5 2-3=-1$$

The solution is the pair that gives sum -5.

$$a=-6 b=1$$

Rewrite x^{2}-5x-6 as \left(x^{2}-6x\right)+\left(x-6\right).

$$\left(x^{2}-6x\right)+\left(x-6\right)$$

Factor out x in x^{2}-6x.

$$x\left(x-6\right)+x-6$$

Factor out common term x-6 by using distributive property.

$$\left(x-6\right)\left(x+1\right)$$

Rewrite the complete factored expression.

$$2x\left(x-6\right)\left(x+1\right)$$

Evaluate

$$2x\left(x-6\right)\left(x+1\right)$$