Question

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

Answer 1

`3x(x-2)`

Explanation:

The term `3x^2` can be thought of as `3x*x` and the term `6x` can be thought of as `3x*2`. The `3x` is therefore a common factor that can be factored out (reversing the distributive property), and keeping the minus sign in place: `3x^2-6x=3x(x-2)`.

This also implies that the roots (`x`-intercepts) of the function `f(x)=3x^2-6x=3x(x-2)` are `x=0` and `x=2`.