Question

How do you factor `3x^3 - 3x^2 - 6x`?

Answer 1

`3x^3-3x^2-6x= 3x(x-2)(x+1)`

Explanation:

First, observe that the greatest shared constant factor of each term is `3`, and the highest power of `x` shared by each term is `x^1`. Thus, we start by factoring that out from each term.

`3x^3-3x^2-6x = 3x(x^2-x-2)`

Next, to factor the remaining quadratic expression, there are several techniques. In our case, we will look for two values whose product is equal to the product of the coefficient of `x^2` and the constant term, that is, `1*-2=-2`, and whose sum is equal to the coefficient of `x`, that is, `-1`. Doing so, we find that `-2` and `1` fulfill these conditions, and so we can finish factoring the expression as

`3x(x^2-x-2) = 3x(x-2)(x+1)`