# How do you factor x^3= -3x^2-2x?

Oct 13, 2015

$x \cdot \left(x + 1\right) \cdot \left(x + 2\right) = 0$

#### Explanation:

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

$\iff x \cdot \left({x}^{2} + 3 x + 2\right) = 0$

Now, choose two numbers, whose sum equals the the coefficient of $x$ and whose product is the product of the coefficient of ${x}^{2}$ and the constant.

Here the coefficient of $x$ is $3$
The coefficient of ${x}^{2}$ is $1$
and the constant is $2$

So the numbers are 2 & 1

Thus the above expression can be written as

$x \cdot \left({x}^{2} + 2 x + x + 2\right) = 0$

that is $x \cdot \left\{x \cdot \left(x + 2\right) + 1 \cdot \left(x + 2\right)\right\} = 0$

which in turn can be written as

$x \cdot \left(x + 1\right) \cdot \left(x + 2\right) = 0$